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31181e6 | 1 | {"segments": [{"id": 1, "seek": 1657, "start": 0.07, "end": 16.57, "text": "ุจุณู
ุงููู ุงูุฑุญู
ู ุงูุฑุญูู
ุ ุงูููู
ุฅู ุดุงุก ุงููู ุฑุงุญ ููู
ู ูู chapter ุนุดุฑุฉุ ุจูุญูู .. ุจุฏููุง ุนู ุงู seriesุ ุญูููุง ุจุงูุฃูู ุงู sequence ุทุจุนุงุ ุจุนุฏูู ุงู seriesุ ู ุขุฎุฑ ุฅุดู ุญูููุง ุนู ุงูุฎู
ุณ ูุตุงุฏ ุงููู ุจูุณุชุฎุฏู
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ุฑุงุญ ูุญูู ุนู ุณูููููุณ ุฃุฎุฑู ู
ุด ุงูู Positive Terms ุงููู ูู ุงุณู
ูุง ุงูู Alternating Series ุจูุนุฑู ุฅูุด ูู ุงู Alternating Series ู ููู ูุดูููุง ูู ูู Converge ููุง Diverge ูุฃู ุงู Alternating Series ูู ุนุจุงุฑุฉ ุนู Series in which terms are alternately positive and negative ูุนูู ู
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ุชุฑุฏุฏุฉ term ู
ูุฌุจ ุชุฑู
ุณุงูุจ ู
ูุฌุจ ุณุงูุจ ู
ูุฌุจ ุณุงูุจ ู ููุฐุง ูุนูู ูู ุนุจุงุฑุฉ ุนู ุจูุบุฉ ุฑูุงุถูุฉ summation ููุฅู ู ุงู an ูู an ุฒุงุฆุฏ ูุงุญุฏ ุฃูู ู
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ู", "probability": 0.9931640625}, {"start": 58.57, "end": 58.99, "word": " ุงูุณูุฑ", "probability": 0.6801350911458334}], "temperature": 1.0}, {"id": 4, "seek": 8397, "start": 59.21, "end": 83.97, "text": "ูุนูู a n ู ุงูุนุฏุฏ ุงููู ุจุนุฏู ูุญุฏ ุงู ูููู ู ูุญุฏ ุงู n ุฒุงุฏ ูุงุญุฏ ุญุงุตู ุถุฑุจูู
ุณุงูุจ ูุนูู ูุงุญุฏ ู
ูุฌุจ ูุงูุชุงูู ุณุงูุจ ู
ุด ุงูุชุงููู ุณุงูุจูู ููุง ุงูุชุงููู ู
ูุฌุจูู ูุงุญุฏ ู
ููู
ู
ูุฌุจ ู ุงููู ุจุนุฏู ุจููู ุณุงูุจ ุฃู
ุซู ุนูู ุงูุฃุฑุถ ุงู alternating series ูุนูู ู
ุซูุง the summation ู-1 ุฃุณ n ูุฐู alternating series ูุฐู ุฃุดูุงุก ูุงูุต ูุงุญุฏ ุฒุงุฏ ูุงุญุฏ ูุงูุต ูุงุญุฏ ูุงุญุฏ ูุงูุต ูุงุญุฏ ูุงุญุฏ", "tokens": [40228, 22653, 257, 297, 4032, 18863, 3215, 3215, 13672, 1829, 39182, 3224, 5296, 24401, 2423, 8717, 11536, 1829, 4032, 5296, 24401, 2423, 297, 30767, 18513, 36764, 24401, 11331, 33546, 1211, 48812, 25513, 16095, 8608, 6027, 3555, 37495, 22653, 36764, 24401, 3714, 29245, 3555, 16070, 2655, 7649, 1829, 8608, 6027, 3555, 37893, 16712, 7649, 9957, 8608, 6027, 3555, 9957, 49429, 16712, 7649, 9957, 3714, 29245, 3555, 9957, 36764, 24401, 9154, 16095, 3714, 29245, 3555, 4032, 13672, 1829, 39182, 3224, 4724, 30544, 8608, 6027, 3555, 5551, 2304, 12984, 1211, 15844, 16247, 43042, 2423, 40062, 2638, 37495, 22653, 50113, 15040, 264, 28811, 5296, 12, 16, 5551, 3794, 297, 29538, 40062, 2638, 29538, 5551, 8592, 1829, 16606, 8717, 995, 4587, 9381, 36764, 24401, 30767, 18513, 36764, 24401, 8717, 995, 4587, 9381, 36764, 24401, 36764, 24401, 8717, 995, 4587, 9381, 36764, 24401, 36764, 24401], "avg_logprob": -0.19185267378176962, "compression_ratio": 2.245833333333333, "no_speech_prob": 0.0, "words": [{"start": 59.21, "end": 59.63, "word": "ูุนูู", "probability": 0.73291015625}, {"start": 59.63, "end": 59.87, "word": " a", "probability": 0.209716796875}, {"start": 59.87, "end": 60.07, "word": " n", "probability": 0.2413330078125}, {"start": 60.07, "end": 60.27, "word": " ู", "probability": 0.646484375}, {"start": 60.27, "end": 60.69, "word": " ุงูุนุฏุฏ", "probability": 0.8917643229166666}, {"start": 60.69, "end": 60.83, "word": " ุงููู", "probability": 0.896484375}, {"start": 60.83, "end": 61.33, "word": " ุจุนุฏู", "probability": 0.873291015625}, {"start": 61.33, "end": 61.87, "word": " ูุญุฏ", "probability": 0.688720703125}, {"start": 61.87, "end": 62.13, "word": " ุงู", "probability": 0.38330078125}, {"start": 62.13, "end": 62.47, "word": " ูููู", "probability": 0.6934814453125}, {"start": 62.47, "end": 62.55, "word": " ู", "probability": 0.8916015625}, {"start": 62.55, "end": 62.85, "word": " ูุญุฏ", "probability": 0.943115234375}, {"start": 62.85, "end": 63.23, "word": " ุงู", "probability": 0.8408203125}, {"start": 63.23, "end": 63.43, "word": " n", "probability": 0.7529296875}, {"start": 63.43, "end": 63.69, "word": " ุฒุงุฏ", "probability": 0.201904296875}, {"start": 63.69, "end": 64.11, "word": " ูุงุญุฏ", "probability": 0.914306640625}, {"start": 64.11, "end": 64.77, "word": " ุญุงุตู", "probability": 0.73486328125}, {"start": 64.77, "end": 65.25, "word": " ุถุฑุจูู
", "probability": 0.9435221354166666}, {"start": 65.25, "end": 65.63, "word": " ุณุงูุจ", "probability": 0.9130859375}, {"start": 65.63, "end": 65.91, "word": " ูุนูู", "probability": 0.87109375}, {"start": 65.91, "end": 66.37, "word": " ูุงุญุฏ", "probability": 0.968505859375}, {"start": 66.37, "end": 66.71, "word": " ู
ูุฌุจ", "probability": 0.9794921875}, {"start": 66.71, "end": 67.11, "word": " ูุงูุชุงูู", "probability": 0.8475341796875}, {"start": 67.11, "end": 67.61, "word": " ุณุงูุจ", "probability": 0.9763997395833334}, {"start": 67.61, "end": 67.77, "word": " ู
ุด", "probability": 0.8525390625}, {"start": 67.77, "end": 68.19, "word": " ุงูุชุงููู", "probability": 0.8356119791666666}, {"start": 68.19, "end": 68.73, "word": " ุณุงูุจูู", "probability": 0.906005859375}, {"start": 68.73, "end": 69.21, "word": " ููุง", "probability": 0.8134765625}, {"start": 69.21, "end": 69.57, "word": " ุงูุชุงููู", "probability": 0.9718424479166666}, {"start": 69.57, "end": 69.95, "word": " ู
ูุฌุจูู", "probability": 0.985107421875}, {"start": 69.95, "end": 70.19, "word": " ูุงุญุฏ", "probability": 0.979248046875}, {"start": 70.19, "end": 70.43, "word": " ู
ููู
", "probability": 0.982177734375}, {"start": 70.43, "end": 70.69, "word": " ู
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ุซู", "probability": 0.730712890625}, {"start": 73.19, "end": 73.41, "word": " ุนูู", "probability": 0.95166015625}, {"start": 73.41, "end": 73.73, "word": " ุงูุฃุฑุถ", "probability": 0.847900390625}, {"start": 73.73, "end": 74.09, "word": " ุงู", "probability": 0.9658203125}, {"start": 74.09, "end": 74.57, "word": " alternating", "probability": 0.9619140625}, {"start": 74.57, "end": 75.07, "word": " series", "probability": 0.916015625}, {"start": 75.07, "end": 75.37, "word": " ูุนูู", "probability": 0.92626953125}, {"start": 75.37, "end": 75.67, "word": " ู
ุซูุง", "probability": 0.9482421875}, {"start": 75.67, "end": 75.85, "word": " the", "probability": 0.272216796875}, {"start": 75.85, "end": 76.29, "word": " summation", "probability": 0.89453125}, {"start": 76.29, "end": 76.45, "word": " ู", "probability": 0.90478515625}, {"start": 76.45, "end": 76.93, "word": "-1", "probability": 0.490966796875}, {"start": 76.93, "end": 77.19, "word": " ุฃุณ", "probability": 0.4801025390625}, {"start": 77.19, "end": 77.59, "word": " n", "probability": 0.537109375}, {"start": 77.59, "end": 77.99, "word": " ูุฐู", "probability": 0.5068359375}, {"start": 77.99, "end": 78.61, "word": " alternating", "probability": 0.9833984375}, {"start": 78.61, "end": 79.19, "word": " series", "probability": 0.916015625}, {"start": 79.19, "end": 79.81, "word": " ูุฐู", "probability": 0.84326171875}, {"start": 79.81, "end": 80.33, "word": " ุฃุดูุงุก", "probability": 0.9200439453125}, {"start": 80.33, "end": 80.65, "word": " ูุงูุต", "probability": 0.738037109375}, {"start": 80.65, "end": 81.01, "word": " ูุงุญุฏ", "probability": 0.958251953125}, {"start": 81.01, "end": 81.63, "word": " ุฒุงุฏ", "probability": 0.888427734375}, {"start": 81.63, "end": 82.07, "word": " ูุงุญุฏ", "probability": 0.98876953125}, {"start": 82.07, "end": 82.53, "word": " ูุงูุต", "probability": 0.9583740234375}, {"start": 82.53, "end": 82.83, "word": " ูุงุญุฏ", "probability": 0.991455078125}, {"start": 82.83, "end": 83.07, "word": " ูุงุญุฏ", "probability": 0.97705078125}, {"start": 83.07, "end": 83.41, "word": " ูุงูุต", "probability": 0.9188232421875}, {"start": 83.41, "end": 83.65, "word": " ูุงุญุฏ", "probability": 0.993408203125}, {"start": 83.65, "end": 83.97, "word": " ูุงุญุฏ", "probability": 0.982177734375}], "temperature": 1.0}, {"id": 5, "seek": 11280, "start": 84.2, "end": 112.8, "text": "ุชุชุฑุฏุฏ ุจูู ูุงูุต ูุงุญุฏ ูุงุญุฏ ุจูู ู
ูุฌุจ ู ุณุงูุจ ูู
ุงู ู
ู ุฃู
ุซูุฉ ุงู series ุทุจุนุง ูุซูุฑุฉ ู
ููุง ู
ุซูุง ูุงูุต ูุงุญุฏ ุฃุณูุฒุงุฆุฏ ูุงุญุฏ ุนูู ุฃุฑุจุนุฉ N ุฒุงุฆุฏ ูุงุญุฏ ูุงูู alternating series ูุฅูู ูู term ู
ูุฌุจ ู term ุงูุช ุณุงูู ูุงุญุฏ ุจุทูุน ุงูุงุด ู
ูุฌุจ ูุนูู ู
ุซูุง ุฎู
ุณ N ุชุณุงูู ุงุชููู ุจุทูุน ูุฐู ุณุงูุจ ุณุงูุจ ุชุณุนุฉ ู ููุฐุง ูุนูู ู
ูุฌุจ ุณุงูุจ ู
ูุฌุจ ุณุงูุจ ู ููุฐุง ุงู series ุจุชููู ุจูุฐุง ุงูุดูู", "tokens": [2655, 2655, 2288, 3215, 3215, 49374, 8717, 995, 4587, 9381, 36764, 24401, 36764, 24401, 49374, 3714, 29245, 3555, 4032, 8608, 6027, 3555, 9122, 2304, 7649, 9154, 5551, 2304, 12984, 37977, 2423, 2638, 23032, 3555, 3615, 995, 9122, 12984, 48923, 9154, 11296, 50113, 15040, 8717, 995, 4587, 9381, 36764, 24401, 5551, 3794, 1863, 11622, 16373, 3215, 36764, 24401, 15844, 5551, 25513, 27884, 426, 30767, 16373, 3215, 36764, 24401, 8032, 6027, 1829, 40062, 2638, 5296, 28814, 1863, 3224, 8978, 1433, 3714, 29245, 3555, 4032, 1433, 16472, 2655, 8608, 995, 45865, 36764, 24401, 4724, 9566, 1211, 3615, 1975, 1829, 33599, 3714, 29245, 3555, 37495, 22653, 50113, 15040, 16490, 2304, 3794, 426, 6055, 3794, 995, 45865, 1975, 2655, 1863, 9957, 4724, 9566, 1211, 3615, 29538, 8608, 6027, 3555, 8608, 6027, 3555, 6055, 3794, 27884, 4032, 8032, 4117, 15730, 37495, 22653, 3714, 29245, 3555, 8608, 6027, 3555, 3714, 29245, 3555, 8608, 6027, 3555, 4032, 8032, 4117, 15730, 2423, 2638, 39894, 30544, 39627, 15730, 25124, 28820], "avg_logprob": -0.210403729669796, "compression_ratio": 2.13671875, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 84.2, "end": 84.84, "word": "ุชุชุฑุฏุฏ", "probability": 0.90166015625}, {"start": 84.84, "end": 85.0, "word": " ุจูู", "probability": 0.8857421875}, {"start": 85.0, "end": 85.36, "word": " ูุงูุต", "probability": 0.77227783203125}, {"start": 85.36, "end": 85.62, "word": " ูุงุญุฏ", "probability": 0.823486328125}, {"start": 85.62, "end": 86.0, "word": " ูุงุญุฏ", "probability": 0.8203125}, {"start": 86.0, "end": 86.28, "word": " ุจูู", "probability": 0.44482421875}, {"start": 86.28, "end": 86.6, "word": " ู
ูุฌุจ", "probability": 0.9690755208333334}, {"start": 86.6, "end": 86.8, "word": " ู", "probability": 0.6904296875}, {"start": 86.8, "end": 87.3, "word": " ุณุงูุจ", "probability": 0.8043619791666666}, {"start": 87.3, "end": 88.24, "word": " ูู
ุงู", "probability": 0.9013671875}, {"start": 88.24, "end": 88.44, "word": " ู
ู", "probability": 0.95751953125}, {"start": 88.44, "end": 88.88, "word": " ุฃู
ุซูุฉ", "probability": 0.9473876953125}, {"start": 88.88, "end": 89.08, "word": " ุงู", "probability": 0.857421875}, {"start": 89.08, "end": 89.26, "word": " series", "probability": 0.7783203125}, {"start": 89.26, "end": 89.56, "word": " ุทุจุนุง", "probability": 0.957763671875}, {"start": 89.56, "end": 90.04, "word": " ูุซูุฑุฉ", "probability": 0.7521158854166666}, {"start": 90.04, "end": 90.44, "word": " ู
ููุง", "probability": 0.91650390625}, {"start": 90.44, "end": 90.7, "word": " ู
ุซูุง", "probability": 0.765625}, {"start": 90.7, "end": 91.02, "word": " ูุงูุต", "probability": 0.9661865234375}, {"start": 91.02, "end": 91.26, "word": " ูุงุญุฏ", "probability": 0.950439453125}, {"start": 91.26, "end": 91.78, "word": " ุฃุณูุฒุงุฆุฏ", "probability": 0.5295206705729166}, {"start": 91.78, "end": 92.08, "word": " ูุงุญุฏ", "probability": 0.98828125}, {"start": 92.08, "end": 92.36, "word": " ุนูู", "probability": 0.697265625}, {"start": 92.36, "end": 93.18, "word": " ุฃุฑุจุนุฉ", "probability": 0.76318359375}, {"start": 93.18, "end": 93.44, "word": " N", "probability": 0.352294921875}, {"start": 93.44, "end": 94.08, "word": " ุฒุงุฆุฏ", "probability": 0.90869140625}, {"start": 94.08, "end": 94.62, "word": " ูุงุญุฏ", "probability": 0.984619140625}, {"start": 94.62, "end": 94.88, "word": " ูุงูู", "probability": 0.585693359375}, {"start": 94.88, "end": 95.34, "word": " alternating", "probability": 0.88720703125}, {"start": 95.34, "end": 95.92, "word": " series", "probability": 0.88134765625}, {"start": 95.92, "end": 96.84, "word": " ูุฅูู", "probability": 0.794189453125}, {"start": 96.84, "end": 97.46, "word": " ูู", "probability": 0.88427734375}, {"start": 97.46, "end": 97.74, "word": " term", "probability": 0.93310546875}, {"start": 97.74, "end": 97.98, "word": " ู
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ูู ุฅููุง ู ูุดูููุง converge ููุง diverge ุทุจุนุง ูู ูุชุจูุง ุงู alternating series ุจุดูู ู
ุงููุต ูุงุญุฏ ุฃุณ ุฅู ุฒุงุฆุฏ ูุงุญุฏ UN ูุนูู ุงูู
ููููุฉ ูุฐู ูู ูุงุญุฏ ูุงูุต ูู ุงุชููู ุฒุงุฆุฏ ูู ุชูุงุชุฉ ูุงูุต ูู ุฃุฑุจุนุฉ ุฅูู ุฃุฎุฑูู ุงูุงู ูุฐู .. ุจุชููู ุงู series ูุฐู ุจูุณู
ููุง ุทุจุนุง alternating series ูู ู
ุชุฑุฏุฏุฉ ุจูู ู
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ูุฉ ุฃูู ุดุฑุท ุฃู all ุงู UNs are positive ุงู UN ูุฏููุฉ ูููู
ุ ูุนูู U1 ู U2ุ ุจุบุถ ุงููุธุฑ ุนู ุงูุฅุดุงุฑุฉุ ุจุณ ุงู U ุงู U ูุฏููุฉ ูููู
ูููููุง ู
ูุฌุจููุ ูุจูู ุงู UN ุฃุดูู ุงููุงูุตุ ุจูุดูู ุงููุงูุต ูุงุญุฏ ุฃุณ ุฅุฒุงุนุฏ ูุงุญุฏุ ู ุงู UN ูุฐู ุชูุฃุด ุชููู ูุญุงููุง ู
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ุฉ decreasing ู non-increasingุ ุจุงููุณุงูู ุงูุขู ุจุงู decreasing ูุนูู UN ุฃูุจุฑ ู
ู UN ุฒุงุฆุฏ ูุงุญุฏ ุจุชููู decreasing ูุนูู ุฃูุด ูู ู
ุงููุง ุงูุฃุนุฏุงุฏ ุจุชุตุบุฑ ู
ุงููุด ุชุณุงูู ููู
ุฅุฐุง ูุงู ูุฌุฏ ุชุณุงูู ุจูุณู
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ู
ูู ุงู UN ุชุณุงูู ุงู UN ุฒุงุฆุฏ ูุงุญุฏ ูู ููุฑุฉ ูุจุชุตูุฑ ู
ุด decreasing ุจุชููู non increasing ุญุชู ูู ูุงูุช non increasing ูููุง ุชุณุงูู ู
ุงููุด ุนูุฏูุง ู
ุดููุฉ ุจุชููู ูุฐุง ุงูุดุฑุท ุชููุฑ for all in ุฃูุจุฑ ุฃูู ุณุงูู in ูุนูู ูุฃู ููุทุฉ in ู
ู
ูู ู
ุงุชูููุด ู
ู ุจุฏุงูุฉ ุงู series ู
ู ุงููุงุญุฏ ุชููู ู
ู ุจุฏุงูุฉ ุฃุฎุฑู ู
ุด ู
ุดููุฉ for some integer in ุงูุดุฑุท ุงูุซุงูุซ ุงูู limit ุงู UN ูุณุงูู ุณูุฑ limit ุงู UN ูุงุฒู
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27276, "start": 243.42, "end": 272.76, "text": "ุงูุงู ุจุฏูุง ูุทุจู ุงู UN ูุงุฏ ูุทุจู ุนูููุง ุงูุชูุงุช ุดุฑูุท ุฅุฐุง ูุงู ูุทุจู ุนูููุง ุงูุชูุงุช ุดุฑูุท ุจุชููู ุงู series converged ูุฃู ุงู UN ูู ุนุจุงุฑุฉ ุนู ูู ูุงุญุฏ ุฒุงุฆุฏ ูุงุญุฏ ุนูู N ูุจุฏุฃุช ุงู series ุชุจุนุชูุง ู
ู ูุงุญุฏ ุฅูู ู
ูุงููู ูุนูู ูุดูู ูุทุจู ุงูุดุฑูุท ุฅู
ุง ุจุชูุทุจู ู
ู ูุงุญุฏ ุฃู ุจุนุฏ ุงููุงุญุฏ ู
ุด ู
ุดููุฉ ุฃูู ุฅุดู ุงู UN ูู ูุงุญุฏ ุฒุงุฆุฏ ูุงุญุฏ ุนูู N ูู
ุง N ุฃูุจุฑ ุฃู ุณูู ูุงุญุฏ ูู
ุง N ุชุณูู ูุงุญุฏ ูุนูู ุจูุตูุฑูุง ุฏู ุจุงุฏูุฉ ู
ู ูู ุงุชููู ูุจุนุฏูู ูู
ุง ููู ูุต ุจูุตูุฑ ูู ูุงุญุฏ ููุต ููุง ูุฏู ูู ูุฏููุฉ ูุนูู ุฃูุจุฑ ู
ู ูุงุญุฏ ูุฅูู ุฒุฏุช ู
ูุฏุงุฑ ู
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ู ูุงุญุฏ ู ุจุนุฏ ุงููุงุญุฏ ููู ุจููุฉ ู
ูุฌุจุฉ ุฅุฐุง ุงู N ุชุจุนุช ูุงุฏู ู
ูุฌุจุฉ for all N ุฃูุจุฑ ุฃู ุณุงูู ุงููุงุญุฏ ูุฃู ุนุดุงู ูุดูู ุงู decrement ุจุฏูุง ูุฌูุจ ุงูู
ุดุชูุฉ ุงูู
ุดุชูุฉ ููุง ูุงุญุฏ ุนูู ูุงุญุฏ ุฒุงุฏ N ูู ูุงุทุณ ูุงุญุฏ ุนูู N ุชุฑููุฉ ุทุจุนุง ุจุฏูู ู
ุง ูุฌู
ุนูุง ูููู ูุฌูุฏ ุงูุฅุดุงุฑุฉ ุงูุณุงูุจุฉ ุทุจุนุง ุงู N ุฏุงุฆู
ุง ู
ูุฌุจุฉ ู ูุฐุง ู
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ุทุจูุฉุ ูุจุงูุชุงูู ุงู series ุชุจุนุชูุง convergeุ ุทูุจุ ุงูุขู ุงู conversion ุชุจุนุชู ุงู series ุงู alternating series ูุฐู ุฅููุง ุฅููุง ููุนูู", "tokens": [6027, 8592, 2288, 9566, 6024, 104, 6027, 12984, 14739, 3224, 4948, 2423, 39184, 8229, 7251, 3794, 995, 45865, 8608, 5172, 2288, 2423, 7649, 4948, 5296, 1863, 2423, 14407, 24401, 30767, 16373, 3215, 36764, 24401, 15844, 426, 23032, 3555, 3615, 995, 39894, 3215, 9778, 1211, 2423, 4948, 5296, 7435, 14407, 12399, 29538, 4948, 11296, 8608, 5172, 2288, 12399, 4724, 1829, 19913, 1211, 5296, 1863, 2423, 14407, 24401, 12399, 7251, 3555, 4587, 7578, 2423, 4948, 46740, 15730, 7251, 3794, 995, 45865, 5296, 1863, 2423, 14407, 24401, 12399, 4032, 5296, 1863, 2423, 14407, 24401, 7251, 3794, 995, 45865, 8608, 5172, 2288, 12399, 11933, 15730, 16712, 1211, 9307, 25124, 32887, 9566, 6055, 3555, 34268, 8315, 3714, 9566, 3555, 28671, 12399, 46599, 6027, 2655, 6027, 1829, 2423, 2638, 6055, 3555, 34268, 8315, 41881, 12399, 23032, 1829, 3555, 12399, 6024, 48506, 2423, 14298, 6055, 3555, 3615, 31371, 2423, 2638, 2423, 40062, 2638, 29538, 11933, 1211, 11296, 11933, 1211, 11296, 8717, 45367, 9957], "avg_logprob": -0.28542992947207896, "compression_ratio": 2.0559701492537314, "no_speech_prob": 0.0, "words": [{"start": 299.26, "end": 299.76, "word": "ุงูุดุฑุท", "probability": 0.87109375}, {"start": 299.76, "end": 300.14, "word": " ุงูุซุงูุซ", "probability": 0.84002685546875}, {"start": 300.14, "end": 300.38, "word": " ุฃูู", "probability": 0.19915771484375}, {"start": 300.38, "end": 300.56, "word": " limit", "probability": 0.77685546875}, {"start": 300.56, "end": 300.78, "word": " ุงูู", "probability": 0.3648681640625}, {"start": 300.78, "end": 301.02, "word": " UN", "probability": 0.40673828125}, {"start": 301.02, "end": 301.42, "word": " ูุณุงูู", "probability": 0.8433837890625}, {"start": 301.42, "end": 301.72, "word": " ุณูุฑ", "probability": 0.7131754557291666}, {"start": 301.72, "end": 302.0, "word": " ุงูุงู", "probability": 0.4981689453125}, {"start": 302.0, "end": 302.32, "word": " limit", "probability": 0.876953125}, {"start": 302.32, "end": 302.58, "word": " ูู", "probability": 0.54931640625}, {"start": 302.58, "end": 302.92, "word": " ุงููุงุญุฏ", "probability": 0.7705078125}, {"start": 302.92, "end": 303.2, "word": " ุฒุงุฆุฏ", "probability": 0.7445475260416666}, {"start": 303.2, "end": 303.48, "word": " ูุงุญุฏ", "probability": 0.962646484375}, {"start": 303.48, "end": 303.62, "word": " ุนูู", "probability": 0.7685546875}, {"start": 303.62, "end": 303.86, "word": " N", "probability": 0.59228515625}, {"start": 303.86, "end": 304.52, "word": " ุทุจุนุง", "probability": 0.894287109375}, {"start": 304.52, "end": 305.02, "word": " ุจุชุฏุฎู", "probability": 0.9078369140625}, {"start": 305.02, "end": 305.12, "word": " ุงู", "probability": 0.64599609375}, {"start": 305.12, "end": 305.36, "word": " limit", "probability": 0.93017578125}, {"start": 305.36, "end": 306.1, "word": " ูุฌูุงุ", "probability": 0.67254638671875}, {"start": 306.1, "end": 306.32, "word": " ูุฐู", "probability": 0.50732421875}, {"start": 306.32, "end": 306.66, "word": " limitูุง", "probability": 0.680908203125}, {"start": 306.66, "end": 307.12, "word": " ุณูุฑุ", "probability": 0.873291015625}, {"start": 307.12, "end": 307.38, "word": " ุจูุธู", "probability": 0.5850830078125}, {"start": 307.38, "end": 307.54, "word": " ูู", "probability": 0.679443359375}, {"start": 307.54, "end": 308.16, "word": " ุงููุงุญุฏุ", "probability": 0.90478515625}, {"start": 308.16, "end": 308.38, "word": " ูุจูู", "probability": 0.95703125}, {"start": 308.38, "end": 308.48, "word": " ุงู", "probability": 0.69091796875}, {"start": 308.48, "end": 308.7, "word": " limit", "probability": 0.97021484375}, {"start": 308.7, "end": 308.98, "word": " ููุฐุง", "probability": 0.718017578125}, {"start": 308.98, "end": 309.24, "word": " ูุณุงูู", "probability": 0.979248046875}, {"start": 309.24, "end": 309.46, "word": " ูู", "probability": 0.960693359375}, {"start": 309.46, "end": 310.24, "word": " ุงููุงุญุฏุ", "probability": 0.84881591796875}, {"start": 310.24, "end": 310.3, "word": " ู", "probability": 0.8173828125}, {"start": 310.3, "end": 310.46, "word": " ูู", "probability": 0.90234375}, {"start": 310.46, "end": 310.82, "word": " ุงููุงุญุฏ", "probability": 0.9925130208333334}, {"start": 310.82, "end": 311.32, "word": " ูุณุงูู", "probability": 0.979248046875}, {"start": 311.32, "end": 312.26, "word": " ุณูุฑุ", "probability": 0.9110107421875}, {"start": 312.26, "end": 312.52, "word": " ุฅุฐุง", "probability": 0.666259765625}, {"start": 312.52, "end": 313.02, "word": " ุงูุชูุงุช", "probability": 0.8201497395833334}, {"start": 313.02, "end": 313.28, "word": " ุงูุดุฑูุท", "probability": 0.8079427083333334}, {"start": 313.28, "end": 313.68, "word": " ุชุจุนุชูุง", "probability": 0.8385009765625}, {"start": 313.68, "end": 314.26, "word": " ู
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ุง absolute ุฃู conditional ูุจูู ุงู converge ุชุจุนุชูุง ุฅู
ุง ุจุชููู absolute ุฃู conditional conversion ุทุจ ููู ุจุฏูุง ูุดูููุง ููุน ุงู convergence ุชุจุนูุง ูู ูู absolute ููุง conditional ุจุฏูุง ูุชุจุน ุงูุงุฎุชุจุงุฑ ุงูุชุงูู ุจูุณู
ู ุงู series ุชุจุนุชูุง ูุตู
ู
ุด ููุงู converge absolutely ุฃู absolutely convergent if the corresponding series of absolute value ูุตู
ู
ุด ููabsolute value ููุงู converges", "tokens": [41185, 8717, 45367, 9957, 11933, 1211, 11296, 11933, 15042, 8236, 34051, 27708, 7251, 3555, 4587, 7578, 2423, 41881, 6055, 3555, 34268, 8315, 11933, 15042, 39894, 30544, 8236, 34051, 27708, 14298, 23032, 3555, 9122, 33911, 47525, 8315, 8717, 8592, 38688, 11296, 8717, 45367, 2423, 32181, 6055, 3555, 3615, 11296, 8032, 1211, 31439, 8236, 49429, 27708, 47525, 8315, 8717, 2655, 3555, 3615, 2423, 47283, 2655, 3555, 9640, 16712, 6027, 1829, 44945, 38251, 1829, 2423, 2638, 6055, 3555, 34268, 8315, 5296, 9381, 2304, 2304, 8592, 24976, 7649, 41881, 3122, 34051, 3122, 9652, 6930, 498, 264, 11760, 2638, 295, 8236, 2158, 5296, 9381, 2304, 2304, 8592, 24976, 17243, 401, 1169, 2158, 24976, 7649, 9652, 2880], "avg_logprob": -0.26548548974096775, "compression_ratio": 2.0617283950617282, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 325.84, "end": 326.06, "word": "ูู", "probability": 0.28759765625}, {"start": 326.06, "end": 326.46, "word": " ููุนูู", "probability": 0.9112955729166666}, {"start": 326.46, "end": 326.7, "word": " ุฅููุง", "probability": 0.5965983072916666}, {"start": 326.7, "end": 327.1, "word": " ุฅู
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ู
ุด", "probability": 0.54140625}, {"start": 343.88, "end": 344.26, "word": " ููุงู", "probability": 0.386199951171875}, {"start": 344.26, "end": 344.76, "word": " converge", "probability": 0.9521484375}, {"start": 344.76, "end": 345.48, "word": " absolutely", "probability": 0.64697265625}, {"start": 345.48, "end": 346.08, "word": " ุฃู", "probability": 0.88671875}, {"start": 346.08, "end": 346.72, "word": " absolutely", "probability": 0.70654296875}, {"start": 346.72, "end": 347.64, "word": " convergent", "probability": 0.631591796875}, {"start": 347.64, "end": 348.34, "word": " if", "probability": 0.91015625}, {"start": 348.34, "end": 348.52, "word": " the", "probability": 0.8974609375}, {"start": 348.52, "end": 349.12, "word": " corresponding", "probability": 0.75537109375}, {"start": 349.12, "end": 349.58, "word": " series", "probability": 0.92724609375}, {"start": 349.58, "end": 349.94, "word": " of", "probability": 0.9755859375}, {"start": 349.94, "end": 350.42, "word": " absolute", "probability": 0.92236328125}, {"start": 350.42, "end": 350.96, "word": " value", "probability": 0.96875}, {"start": 350.96, "end": 351.68, "word": " ูุตู
ู
ุด", "probability": 0.83291015625}, {"start": 351.68, "end": 352.36, "word": " ููabsolute", "probability": 0.7808837890625}, {"start": 352.36, "end": 352.66, "word": " value", "probability": 0.9345703125}, {"start": 352.66, "end": 353.08, "word": " ููุงู", "probability": 0.49169921875}, {"start": 353.08, "end": 353.82, "word": " converges", "probability": 0.783447265625}], "temperature": 1.0}, {"id": 15, "seek": 38287, "start": 354.31, "end": 382.87, "text": "ูุนูู ูู ุฃุฎุฏูุง ุงูุงู ุฏู ู ุญุทููุงูุง ุฏุงุฎู absolute value ุตุงุฑุช series of positive terms ุงู series of positive terms ูุฐู ู
ู
ูู ูุนู
ููุง ุฃู ูุงุญุฏ ู
ู ุงูุชุณุชุงุช ุงูุฎู
ุณุฉ ุงูุณุงุฏูุฉ ุฅุฐุง ูุงู ุนู
ูุช ุฃู test ู
ู ุงูุชุณุชุงุช ุงูุฎู
ุณุฉ ู ุทูุนุช converge ุจูุณู
ู ุงู series ุชุจุนุชูุง ูุฐู converge absolutely ูุจูู ุจุชููู converge absolutely ุฅุฐุง ูุงูุช ุงู series of positive terms ุชุจุนุชูุง ูุนูู ูู
ุง ุฃุฎุฏ ุงู absolute value ุชููู converge ุจุฃู ู
ู ุงูุชุณุชุงุช ุงูุฎู
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ู", "probability": 0.98779296875}, {"start": 366.93, "end": 367.33, "word": " ุงูุชุณุชุงุช", "probability": 0.9734700520833334}, {"start": 367.33, "end": 367.73, "word": " ุงูุฎู
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ู", "probability": 0.98974609375}, {"start": 381.63, "end": 382.25, "word": " ุงูุชุณุชุงุช", "probability": 0.9773763020833334}, {"start": 382.25, "end": 382.87, "word": " ุงูุฎู
ุณุฉ", "probability": 0.991943359375}], "temperature": 1.0}, {"id": 16, "seek": 38833, "start": 383.55, "end": 388.33, "text": "ุทูุจ ุฅุฐุง ูุงู ุทูุนุช ู
ุนุงู ุฏุงูููุฑุฌ", "tokens": [9566, 1829, 3555, 11933, 15730, 25961, 23032, 1211, 34268, 20449, 40294, 11778, 995, 33911, 13546, 7435], "avg_logprob": -0.38556985294117646, "compression_ratio": 0.8833333333333333, "no_speech_prob": 0.0, "words": [{"start": 383.55, "end": 383.97, "word": "ุทูุจ", "probability": 0.778076171875}, {"start": 383.97, "end": 384.21, "word": " ุฅุฐุง", "probability": 0.806640625}, {"start": 384.21, "end": 384.89, "word": " ูุงู", "probability": 0.9814453125}, {"start": 384.89, "end": 385.27, "word": " ุทูุนุช", "probability": 0.7495930989583334}, {"start": 385.27, "end": 385.55, "word": " ู
ุนุงู", "probability": 0.84912109375}, {"start": 385.55, "end": 388.33, "word": " ุฏุงูููุฑุฌ", "probability": 0.5755859375}], "temperature": 1.0}, {"id": 17, "seek": 41420, "start": 388.92, "end": 414.2, "text": "ุจุฑูุญ ุจุทุจู ุงูุชูุงุช ุดุฑูุท ูุจูู ูุงู ุงูู ุนุดุงู ุงู definition ุงูุชุงูู ุงู
ุชู ุจุชููู converge conditionally ุงู series that converges but does not converge absolutely ูุจูู ูู ู
ุด converge absolutely ุนุดุงู ูุนูู ู
ุด converge absolutely ูุนูู ุจุงู absolute value diverse ุจุชููู ู ุงูุชูุงุช ุดุฑูุท ู ูู converge ูุนูู ุงูุชูุงุช ุดุฑูุท ุชุจุนุชูุง ุงุชุญููุช ูู ุงููุธุฑูุฉ ุงูุณุงุจูุฉ ูุจูุณู
ู ุงู series ูู ูุฐู ุงูุญุงูุฉ converge conditionally", "tokens": [3555, 32887, 5016, 4724, 9566, 3555, 4587, 16712, 1211, 9307, 13412, 32887, 9566, 7251, 3555, 4587, 7578, 8032, 47302, 1975, 1829, 3224, 6225, 8592, 7649, 2423, 7123, 16712, 7649, 1829, 1975, 2304, 49975, 39894, 30544, 41881, 4188, 379, 2423, 2638, 300, 9652, 2880, 457, 775, 406, 41881, 3122, 7251, 3555, 4587, 7578, 39896, 37893, 41881, 3122, 6225, 8592, 7649, 37495, 22653, 37893, 41881, 3122, 37495, 22653, 20666, 8236, 2158, 9521, 39894, 30544, 4032, 16712, 1211, 9307, 13412, 32887, 9566, 4032, 39896, 41881, 37495, 22653, 16712, 1211, 9307, 13412, 32887, 9566, 6055, 3555, 34268, 8315, 1975, 2655, 5016, 4587, 38149, 8978, 28239, 19913, 2288, 10632, 21136, 16758, 28671, 6156, 3555, 1863, 38251, 1829, 2423, 2638, 8978, 29538, 21542, 6027, 3660, 41881, 4188, 379], "avg_logprob": -0.2611788608194367, "compression_ratio": 2.1171875, "no_speech_prob": 2.980232238769531e-07, "words": [{"start": 388.92, "end": 389.54, "word": "ุจุฑูุญ", "probability": 0.505859375}, {"start": 389.54, "end": 390.02, "word": " ุจุทุจู", "probability": 0.7681884765625}, {"start": 390.02, "end": 390.38, "word": " ุงูุชูุงุช", "probability": 0.6996256510416666}, {"start": 390.38, "end": 390.7, "word": " ุดุฑูุท", "probability": 0.87890625}, {"start": 390.7, "end": 390.96, "word": " ูุจูู", "probability": 0.80023193359375}, {"start": 390.96, "end": 391.16, "word": " ูุงู", "probability": 0.6669921875}, {"start": 391.16, "end": 391.3, "word": " ุงูู", "probability": 0.6215006510416666}, {"start": 391.3, "end": 391.46, "word": " ุนุดุงู", "probability": 0.6224772135416666}, {"start": 391.46, "end": 391.58, "word": " ุงู", "probability": 0.89892578125}, {"start": 391.58, "end": 391.88, "word": " definition", "probability": 0.74560546875}, {"start": 391.88, "end": 392.34, "word": " ุงูุชุงูู", "probability": 0.8089192708333334}, {"start": 392.34, "end": 392.58, "word": " ุงู
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ุด", "probability": 0.96923828125}, {"start": 399.28, "end": 399.72, "word": " converge", "probability": 0.92138671875}, {"start": 399.72, "end": 400.18, "word": " absolutely", "probability": 0.685546875}, {"start": 400.18, "end": 400.42, "word": " ุนุดุงู", "probability": 0.7218424479166666}, {"start": 400.42, "end": 400.58, "word": " ูุนูู", "probability": 0.80078125}, {"start": 400.58, "end": 400.7, "word": " ู
ุด", "probability": 0.9423828125}, {"start": 400.7, "end": 401.14, "word": " converge", "probability": 0.89892578125}, {"start": 401.14, "end": 401.66, "word": " absolutely", "probability": 0.728515625}, {"start": 401.66, "end": 402.12, "word": " ูุนูู", "probability": 0.8876953125}, {"start": 402.12, "end": 402.5, "word": " ุจุงู", "probability": 0.9375}, {"start": 402.5, "end": 402.82, "word": " absolute", "probability": 0.82763671875}, {"start": 402.82, "end": 403.18, "word": " value", "probability": 0.98828125}, {"start": 403.18, "end": 404.22, "word": " diverse", "probability": 0.2095947265625}, {"start": 404.22, "end": 405.9, "word": " ุจุชููู", "probability": 0.57745361328125}, {"start": 405.9, "end": 406.1, "word": " ู", "probability": 0.368408203125}, {"start": 406.1, "end": 406.62, "word": " ุงูุชูุงุช", "probability": 0.900390625}, {"start": 406.62, "end": 406.92, "word": " ุดุฑูุท", "probability": 0.9619140625}, {"start": 406.92, "end": 407.02, "word": " ู", "probability": 0.63232421875}, {"start": 407.02, "end": 407.16, "word": " ูู", "probability": 0.81005859375}, {"start": 407.16, "end": 407.72, "word": " converge", "probability": 0.94873046875}, {"start": 407.72, "end": 408.08, "word": " ูุนูู", "probability": 0.92041015625}, {"start": 408.08, "end": 408.7, "word": " ุงูุชูุงุช", "probability": 0.95068359375}, {"start": 408.7, "end": 408.94, "word": " ุดุฑูุท", "probability": 0.98095703125}, {"start": 408.94, "end": 409.3, "word": " ุชุจุนุชูุง", "probability": 0.8870849609375}, {"start": 409.3, "end": 409.86, "word": " ุงุชุญููุช", "probability": 0.8892578125}, {"start": 409.86, "end": 410.1, "word": " ูู", "probability": 0.6533203125}, {"start": 410.1, "end": 410.48, "word": " ุงููุธุฑูุฉ", "probability": 0.97265625}, {"start": 410.48, "end": 411.02, "word": " ุงูุณุงุจูุฉ", "probability": 0.99365234375}, {"start": 411.02, "end": 412.0, "word": " ูุจูุณู
ู", "probability": 0.943359375}, {"start": 412.0, "end": 412.16, "word": " ุงู", "probability": 0.96337890625}, {"start": 412.16, "end": 412.38, "word": " series", "probability": 0.94091796875}, {"start": 412.38, "end": 412.56, "word": " ูู", "probability": 0.6513671875}, {"start": 412.56, "end": 412.66, "word": " ูุฐู", "probability": 0.751953125}, {"start": 412.66, "end": 412.96, "word": " ุงูุญุงูุฉ", "probability": 0.939453125}, {"start": 412.96, "end": 413.46, "word": " converge", "probability": 0.9619140625}, {"start": 413.46, "end": 414.2, "word": " conditionally", "probability": 0.89794921875}], "temperature": 1.0}, {"id": 18, "seek": 44242, "start": 415.16, "end": 442.42, "text": "ุฅูุด ูุนูู conditional ูุนูู ุจุงู conditions ูุนูู ุจุงูุดุฑูุท ูุนูู ูู converge ุจุงูุดุฑูุท ูุงู absolutely converge ุจุงู absolute value ูุนูู ุจุงู .. ุจุงู .. ุจุฅูู ุชููู ุงู series of positives ูุนูู converge conditionally ูุนูู converge ุจุงูุชูุช ุดุฑูุท ููุท ูุงู absolutely diverse ูุงุฒู
ูููู ุงู absolutely diverse ุทุจุนุง ุทูุจ ุงูุขู ูู
ุง ูููู ุงู series of positives converge ูุฐู ุจุชููู ุจุฑุถู converge ุจุณ not absolutely ูุนูู ูุฐู converge ุฅูุด ูุนูู", "tokens": [28814, 1829, 8592, 37495, 22653, 27708, 37495, 22653, 20666, 4487, 37495, 22653, 20666, 46309, 2407, 9566, 37495, 22653, 39896, 41881, 20666, 46309, 2407, 9566, 16070, 3122, 41881, 20666, 8236, 2158, 37495, 22653, 20666, 4386, 20666, 4386, 4724, 28814, 1863, 3224, 6055, 30544, 2423, 2638, 295, 35127, 37495, 22653, 41881, 4188, 379, 37495, 22653, 41881, 20666, 2655, 1211, 2655, 13412, 32887, 9566, 6156, 47432, 16070, 3122, 9521, 5296, 31377, 2304, 7251, 30544, 2423, 3122, 9521, 23032, 3555, 3615, 995, 23032, 1829, 3555, 6024, 48506, 5296, 15042, 8717, 30544, 2423, 2638, 295, 35127, 41881, 29538, 39894, 30544, 4724, 43042, 3224, 41881, 4724, 3794, 406, 3122, 37495, 22653, 29538, 41881, 11933, 1829, 8592, 37495, 22653], "avg_logprob": -0.23866150231487984, "compression_ratio": 2.427947598253275, "no_speech_prob": 0.0, "words": [{"start": 415.16, "end": 415.46, "word": "ุฅูุด", "probability": 0.6001993815104166}, {"start": 415.46, "end": 415.6, "word": " ูุนูู", "probability": 0.87255859375}, {"start": 415.6, "end": 416.06, "word": " conditional", "probability": 0.7900390625}, {"start": 416.06, "end": 416.28, "word": " ูุนูู", "probability": 0.7081298828125}, {"start": 416.28, "end": 416.42, "word": " ุจุงู", "probability": 0.9716796875}, {"start": 416.42, "end": 416.9, "word": " conditions", "probability": 0.732421875}, {"start": 416.9, "end": 417.14, "word": " ูุนูู", "probability": 0.76318359375}, {"start": 417.14, "end": 417.68, "word": " ุจุงูุดุฑูุท", "probability": 0.828857421875}, {"start": 417.68, "end": 418.28, "word": " ูุนูู", "probability": 0.772705078125}, {"start": 418.28, "end": 418.48, "word": " ูู", "probability": 0.70068359375}, {"start": 418.48, "end": 418.96, "word": " converge", "probability": 0.71923828125}, {"start": 418.96, "end": 419.74, "word": " ุจุงูุดุฑูุท", "probability": 0.901611328125}, {"start": 419.74, "end": 420.44, "word": " ูุงู", "probability": 0.72021484375}, {"start": 420.44, "end": 421.1, "word": " absolutely", "probability": 0.389404296875}, {"start": 421.1, "end": 421.64, "word": " converge", "probability": 0.9140625}, {"start": 421.64, "end": 422.0, "word": " ุจุงู", "probability": 0.9931640625}, {"start": 422.0, "end": 422.44, "word": " absolute", "probability": 0.78466796875}, {"start": 422.44, "end": 422.94, "word": " value", "probability": 0.98681640625}, {"start": 422.94, "end": 423.48, "word": " ูุนูู", "probability": 0.751953125}, {"start": 423.48, "end": 423.84, "word": " ุจุงู", "probability": 0.6328125}, {"start": 423.84, "end": 423.84, "word": " ..", "probability": 0.442626953125}, {"start": 423.84, "end": 424.4, "word": " ุจุงู", "probability": 0.671875}, {"start": 424.4, "end": 424.7, "word": " ..", "probability": 0.88916015625}, {"start": 424.7, "end": 425.1, "word": " ุจุฅูู", "probability": 0.7293701171875}, {"start": 425.1, "end": 425.34, "word": " ุชููู", "probability": 0.97998046875}, {"start": 425.34, "end": 425.66, "word": " ุงู", "probability": 0.94677734375}, {"start": 425.66, "end": 426.0, "word": " series", "probability": 0.93603515625}, {"start": 426.0, "end": 426.22, "word": " of", "probability": 0.94189453125}, {"start": 426.22, "end": 426.6, "word": " positives", "probability": 0.65771484375}, {"start": 426.6, "end": 427.0, "word": " ูุนูู", "probability": 0.6475830078125}, {"start": 427.0, "end": 427.72, "word": " converge", "probability": 0.6708984375}, {"start": 427.72, "end": 428.38, "word": " conditionally", "probability": 0.837890625}, {"start": 428.38, "end": 428.58, "word": " ูุนูู", "probability": 0.96240234375}, {"start": 428.58, "end": 428.96, "word": " converge", "probability": 0.53662109375}, {"start": 428.96, "end": 429.4, "word": " ุจุงูุชูุช", "probability": 0.73773193359375}, {"start": 429.4, "end": 429.68, "word": " ุดุฑูุท", "probability": 0.966796875}, {"start": 429.68, "end": 430.02, "word": " ููุท", "probability": 0.990966796875}, {"start": 430.02, "end": 430.24, "word": " ูุงู", "probability": 0.80517578125}, {"start": 430.24, "end": 430.74, "word": " absolutely", "probability": 0.7177734375}, {"start": 430.74, "end": 431.34, "word": " diverse", "probability": 0.513671875}, {"start": 431.34, "end": 431.86, "word": " ูุงุฒู
", "probability": 0.9765625}, {"start": 431.86, "end": 432.02, "word": " ูููู", "probability": 0.9921875}, {"start": 432.02, "end": 432.08, "word": " ุงู", "probability": 0.93408203125}, {"start": 432.08, "end": 432.4, "word": " absolutely", "probability": 0.76416015625}, {"start": 432.4, "end": 432.94, "word": " diverse", "probability": 0.900390625}, {"start": 432.94, "end": 434.18, "word": " ุทุจุนุง", "probability": 0.988525390625}, {"start": 434.18, "end": 435.24, "word": " ุทูุจ", "probability": 0.8746744791666666}, {"start": 435.24, "end": 435.82, "word": " ุงูุขู", "probability": 0.66259765625}, {"start": 435.82, "end": 436.14, "word": " ูู
ุง", "probability": 0.96240234375}, {"start": 436.14, "end": 436.46, "word": " ูููู", "probability": 0.751708984375}, {"start": 436.46, "end": 436.6, "word": " ุงู", "probability": 0.955078125}, {"start": 436.6, "end": 436.94, "word": " series", "probability": 0.9658203125}, {"start": 436.94, "end": 437.2, "word": " of", "probability": 0.9765625}, {"start": 437.2, "end": 437.58, "word": " positives", "probability": 0.91796875}, {"start": 437.58, "end": 438.66, "word": " converge", "probability": 0.865234375}, {"start": 438.66, "end": 438.98, "word": " ูุฐู", "probability": 0.5693359375}, {"start": 438.98, "end": 439.36, "word": " ุจุชููู", "probability": 0.8515625}, {"start": 439.36, "end": 439.64, "word": " ุจุฑุถู", "probability": 0.95849609375}, {"start": 439.64, "end": 440.02, "word": " converge", "probability": 0.9873046875}, {"start": 440.02, "end": 440.24, "word": " ุจุณ", "probability": 0.943603515625}, {"start": 440.24, "end": 440.44, "word": " not", "probability": 0.3525390625}, {"start": 440.44, "end": 441.0, "word": " absolutely", "probability": 0.59228515625}, {"start": 441.0, "end": 441.24, "word": " ูุนูู", "probability": 0.96240234375}, {"start": 441.24, "end": 441.44, "word": " ูุฐู", "probability": 0.54150390625}, {"start": 441.44, "end": 441.9, "word": " converge", "probability": 0.97314453125}, {"start": 441.9, "end": 442.14, "word": " ุฅูุด", "probability": 0.9371744791666666}, {"start": 442.14, "end": 442.42, "word": " ูุนูู", "probability": 0.97021484375}], "temperature": 1.0}, {"id": 19, "seek": 47088, "start": 442.78, "end": 470.88, "text": "ูุนูู ูู ุงูุง ุญููุช ุงูุชูุงุช ุดุฑูุทุ ุชุชุญูู ุชููุงุฆููุง ูุจูู ุงูู Absolute convergence test if the summation ูู Absolute ุงูู AN convergesุ then ุงู summation ููู AN convergesุ ุฅูุด ูุนูู ุงู summation ููู AN convergesุ ูุนูู ุชูุทุจู ุนูููุง ุงูุชูุงุช ุดุฑูุทุ ูุนูู ุชูุทุจู ุนูููุง ุงูุชูุงุช ุดุฑูุท ุชูุทุจูุ ูุจูู ุฃู ุณุคุงูุ ุจุณ ููุดุ ุทุจ ููุด ุจูุนู
ู ูุฐุง ุงู testุ ุนูุดุงู ูุดูู ููุน ุงู convergenceุ ูู ูู converge absolutely ููุง conditionallyุ", "tokens": [40228, 22653, 45164, 1975, 8315, 11331, 4587, 38149, 16712, 1211, 9307, 13412, 32887, 9566, 12399, 6055, 2655, 5016, 4587, 4587, 6055, 1211, 4587, 16373, 1829, 14111, 995, 7251, 3555, 4587, 7578, 2423, 39184, 43965, 1169, 32181, 1500, 498, 264, 28811, 5296, 39184, 43965, 1169, 2423, 39184, 5252, 9652, 2880, 12399, 550, 2423, 28811, 24976, 39184, 5252, 9652, 2880, 12399, 11933, 1829, 8592, 37495, 22653, 2423, 28811, 24976, 39184, 5252, 9652, 2880, 22807, 37495, 22653, 6055, 1863, 9566, 3555, 4587, 25894, 11296, 16712, 1211, 9307, 13412, 32887, 9566, 12399, 37495, 22653, 6055, 1863, 9566, 3555, 4587, 25894, 11296, 16712, 1211, 9307, 13412, 32887, 9566, 6055, 1863, 9566, 3555, 4587, 12399, 7251, 3555, 4587, 7578, 36632, 8608, 33604, 6027, 12399, 4724, 3794, 32239, 8592, 22807, 23032, 3555, 32239, 8592, 44945, 25957, 1211, 23758, 2423, 1500, 22807, 11203, 8592, 7649, 8717, 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ุงุณุชูููุง ุดุฑูุท ู
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ุฃุฌูุจ ุจุงู absolute value ุฅุฐุง ูุงู ุจุงู absolute value converge ุจุชููู converge absolutely ู ุจูููู ุฃูุฏู
ุงูุชูุงุช ุดุฑูุท ู
ุชุญููุฉ ููู ูู ูุงูุช ูุฐู ุทูุนุช diverge ูุฐุง ูุง ูุคุฏู ุฅูู ูุฐู ุงู series diverge ุจูุฑูุญ ู
ู ุญูู ุงูุชูุงุช ุดุฑูุท ุฅุฐุง ุชุญูู ุงูุชูุงุช ุดุฑูุท ุจุชููู converge ุฅุฐุง ูู
ูุชุญูููุง ุจุชูููุด diverge ูู
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", "probability": 0.97509765625}, {"start": 505.91, "end": 507.17, "word": " ูุชุญูููุง", "probability": 0.8680419921875}, {"start": 507.17, "end": 507.67, "word": " ุจุชูููุด", "probability": 0.8816731770833334}, {"start": 507.67, "end": 508.23, "word": " diverge", "probability": 0.6815185546875}, {"start": 508.23, "end": 508.55, "word": " ูู
ุงู", "probability": 0.984375}], "temperature": 1.0}, {"id": 22, "seek": 53200, "start": 508.76, "end": 532.0, "text": "ูุฐู ุจุฑุถู ุดุบูุฉ ู
ูู
ุฉ ุงู ุดุฑูุท ุงูุชูุงุซุฉ ุฅุฐุง ูู
ุชุชุญูู ูุง ูุคุฏู ุงูู ูุตุจุญ diversified ูุงุฒู
ุฃูุฌู ุงูู test ุงุฎุฑ ุงู test ุงุฎุฑ ุงููู ููุช ุฑุงุญ ูุดูู ููู ู
ู ุฎูุงู ุงูุฃู
ุซูุฉ ูุนูู ุงู ุงูุชูุงุช ุดุฑูุท ูุฐู ูู ุงูุชูุงุช ุดุฑูุท ุงููู ููุง ูุฑุฌุน ููุง ููุชูุงุช ุดุฑูุท ุงู ุงูุชูุงุช ุดุฑูุท ูุฐู", "tokens": [3224, 24192, 4724, 43042, 3224, 13412, 17082, 37977, 3714, 16095, 3660, 16472, 13412, 32887, 9566, 16712, 1863, 5718, 104, 3660, 11933, 15730, 32767, 6055, 2655, 5016, 4587, 4587, 20193, 7251, 33604, 16254, 16472, 3224, 7251, 9381, 49628, 6111, 2587, 5296, 31377, 2304, 14739, 7435, 3224, 2423, 7578, 1500, 1975, 34740, 2423, 1500, 1975, 34740, 13672, 1829, 12174, 1211, 2655, 12602, 39319, 8717, 8592, 38688, 9122, 33911, 9154, 16490, 1211, 6027, 16247, 2304, 12984, 37977, 37495, 22653, 16472, 16712, 1211, 9307, 13412, 32887, 9566, 29538, 8978, 16712, 1211, 9307, 13412, 32887, 9566, 13672, 1829, 34105, 8717, 47341, 3615, 34105, 24976, 2655, 1211, 9307, 13412, 32887, 9566, 1975, 3224, 16712, 1211, 9307, 13412, 32887, 9566, 29538], "avg_logprob": -0.35516304762467094, "compression_ratio": 1.9473684210526316, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 508.76, "end": 509.24, "word": "ูุฐู", "probability": 0.772705078125}, {"start": 509.24, "end": 509.54, "word": " ุจุฑุถู", "probability": 0.6864827473958334}, {"start": 509.54, "end": 509.84, "word": " ุดุบูุฉ", "probability": 0.7560221354166666}, {"start": 509.84, "end": 510.34, "word": " ู
ูู
ุฉ", "probability": 0.9864908854166666}, {"start": 510.34, "end": 510.78, "word": " ุงู", "probability": 0.2841796875}, {"start": 510.78, "end": 511.22, "word": " ุดุฑูุท", "probability": 0.7752278645833334}, {"start": 511.22, "end": 511.9, "word": " ุงูุชูุงุซุฉ", "probability": 0.61826171875}, {"start": 511.9, "end": 512.42, "word": " ุฅุฐุง", "probability": 0.7919921875}, {"start": 512.42, "end": 512.58, "word": " ูู
", "probability": 0.97119140625}, {"start": 512.58, "end": 513.46, "word": " ุชุชุญูู", "probability": 0.98837890625}, {"start": 513.46, "end": 513.86, "word": " ูุง", "probability": 0.499755859375}, {"start": 513.86, "end": 514.28, "word": " ูุคุฏู", "probability": 0.8974609375}, {"start": 514.28, "end": 514.6, "word": " ุงูู", "probability": 0.61572265625}, {"start": 514.6, "end": 514.84, "word": " ูุตุจุญ", "probability": 0.5438639322916666}, {"start": 514.84, "end": 515.36, "word": " diversified", "probability": 0.167236328125}, {"start": 515.36, "end": 515.6, "word": " ูุงุฒู
", "probability": 0.9005533854166666}, {"start": 515.6, "end": 515.92, "word": " ุฃูุฌู", "probability": 0.5792643229166666}, {"start": 515.92, "end": 516.18, "word": " ุงูู", "probability": 0.6689453125}, {"start": 516.18, "end": 516.42, "word": " test", "probability": 0.90478515625}, {"start": 516.42, "end": 516.96, "word": " ุงุฎุฑ", "probability": 0.6480712890625}, {"start": 516.96, "end": 517.3, "word": " ุงู", "probability": 0.59326171875}, {"start": 517.3, "end": 517.48, "word": " test", "probability": 0.55322265625}, {"start": 517.48, "end": 517.8, "word": " ุงุฎุฑ", "probability": 0.827880859375}, {"start": 517.8, "end": 517.92, "word": " ุงููู", "probability": 0.458709716796875}, {"start": 517.92, "end": 518.04, "word": " ููุช", "probability": 0.5118408203125}, {"start": 518.04, "end": 518.14, "word": " ุฑุงุญ", "probability": 0.74658203125}, {"start": 518.14, "end": 518.4, "word": " ูุดูู", "probability": 0.9749348958333334}, {"start": 518.4, "end": 518.66, "word": " ููู", "probability": 0.906982421875}, {"start": 518.66, "end": 518.8, "word": " ู
ู", "probability": 0.142578125}, {"start": 518.8, "end": 519.26, "word": " ุฎูุงู", "probability": 0.970703125}, {"start": 519.26, "end": 520.12, "word": " ุงูุฃู
ุซูุฉ", "probability": 0.875732421875}, {"start": 520.12, "end": 521.28, "word": " ูุนูู", "probability": 0.67333984375}, {"start": 521.28, "end": 521.88, "word": " ุงู", "probability": 0.72705078125}, {"start": 521.88, "end": 522.76, "word": " ุงูุชูุงุช", "probability": 0.7317708333333334}, {"start": 522.76, "end": 523.04, "word": " ุดุฑูุท", "probability": 0.8766276041666666}, {"start": 523.04, "end": 523.36, "word": " ูุฐู", "probability": 0.642578125}, {"start": 523.36, "end": 523.66, "word": " ูู", "probability": 0.442626953125}, {"start": 523.66, "end": 526.52, "word": " ุงูุชูุงุช", "probability": 0.8937174479166666}, {"start": 526.52, "end": 526.8, "word": " ุดุฑูุท", "probability": 0.9835611979166666}, {"start": 526.8, "end": 526.94, "word": " ุงููู", "probability": 0.84228515625}, {"start": 526.94, "end": 527.28, "word": " ููุง", "probability": 0.97705078125}, {"start": 527.28, "end": 528.48, "word": " ูุฑุฌุน", "probability": 0.7676595052083334}, {"start": 528.48, "end": 528.66, "word": " ููุง", "probability": 0.74560546875}, {"start": 528.66, "end": 529.06, "word": " ููุชูุงุช", "probability": 0.9163818359375}, {"start": 529.06, "end": 530.04, "word": " ุดุฑูุท", "probability": 0.9908854166666666}, {"start": 530.04, "end": 531.0, "word": " ุงู", "probability": 0.61376953125}, {"start": 531.0, "end": 531.38, "word": " ุงูุชูุงุช", "probability": 0.9680989583333334}, {"start": 531.38, "end": 531.66, "word": " ุดุฑูุท", "probability": 0.9913736979166666}, {"start": 531.66, "end": 532.0, "word": " ูุฐู", "probability": 0.81396484375}], "temperature": 1.0}, {"id": 23, "seek": 54965, "start": 532.25, "end": 549.65, "text": "ู
ุงุฐุง ููุง ุจููู ุฅุฐุง ูุงู all three of the following are satisfied ูุจุชููู ุงู series ุชุจุนุชู converge ุฅุฐุง ูุงู ุงูุดุฑูุท ุชุญููุช ูุคุฏู ุฅู ุงู series converge ููู ูู ูู
ุง ุชุญูู ู
ุซูุง ู
ุงูุงููุด ูุฏููุฉ ูููู
positive ููุง ู
ุงููุชุด increasing ู
ุงููุชุด decreasing ูุงูุช increasing", "tokens": [2304, 45636, 995, 34105, 4724, 39648, 11933, 15730, 25961, 439, 1045, 295, 264, 3480, 366, 11239, 6156, 3555, 2655, 30544, 2423, 2638, 6055, 3555, 3615, 31371, 41881, 11933, 15730, 25961, 25124, 32887, 9566, 6055, 5016, 4587, 4587, 2655, 7251, 33604, 16254, 36145, 2423, 2638, 41881, 44381, 45164, 5296, 15042, 6055, 5016, 4587, 4587, 50113, 15040, 19446, 41361, 2407, 8592, 8032, 3215, 12610, 3660, 28242, 16095, 3353, 49429, 19446, 19452, 2655, 8592, 5662, 19446, 19452, 2655, 8592, 23223, 25961, 2655, 5662], "avg_logprob": -0.26851851263164, "compression_ratio": 1.6267281105990783, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 532.25, "end": 532.59, "word": "ู
ุงุฐุง", "probability": 0.6396484375}, {"start": 532.59, "end": 532.71, "word": " ููุง", "probability": 0.2103271484375}, {"start": 532.71, "end": 533.01, "word": " ุจููู", "probability": 0.808349609375}, {"start": 533.01, "end": 533.35, "word": " ุฅุฐุง", "probability": 0.651611328125}, {"start": 533.35, "end": 533.81, "word": " ูุงู", "probability": 0.97705078125}, {"start": 533.81, "end": 534.17, "word": " all", "probability": 0.6259765625}, {"start": 534.17, "end": 534.55, "word": " three", "probability": 0.85009765625}, {"start": 534.55, "end": 534.73, "word": " of", "probability": 0.95263671875}, {"start": 534.73, "end": 534.89, "word": " the", "probability": 0.8779296875}, {"start": 534.89, "end": 535.07, "word": " following", "probability": 0.90380859375}, {"start": 535.07, "end": 535.41, "word": " are", "probability": 0.7158203125}, {"start": 535.41, "end": 536.45, "word": " satisfied", "probability": 0.80517578125}, {"start": 536.45, "end": 537.23, "word": " ูุจุชููู", "probability": 0.8980712890625}, {"start": 537.23, "end": 537.35, "word": " ุงู", "probability": 0.8994140625}, {"start": 537.35, "end": 537.59, "word": " series", "probability": 0.88671875}, {"start": 537.59, "end": 538.05, "word": " ุชุจุนุชู", "probability": 0.8214111328125}, {"start": 538.05, "end": 538.85, "word": " converge", "probability": 0.884765625}, {"start": 538.85, "end": 539.45, "word": " ุฅุฐุง", "probability": 0.934326171875}, {"start": 539.45, "end": 539.71, "word": " ูุงู", "probability": 0.9931640625}, {"start": 539.71, "end": 540.11, "word": " ุงูุดุฑูุท", "probability": 0.74853515625}, {"start": 540.11, "end": 540.93, "word": " ุชุญููุช", "probability": 0.8251953125}, {"start": 540.93, "end": 541.45, "word": " ูุคุฏู", "probability": 0.9075520833333334}, {"start": 541.45, "end": 541.67, "word": " ุฅู", "probability": 0.392578125}, {"start": 541.67, "end": 541.83, "word": " ุงู", "probability": 0.93359375}, {"start": 541.83, "end": 542.11, "word": " series", "probability": 0.9580078125}, {"start": 542.11, "end": 542.63, "word": " converge", "probability": 0.75390625}, {"start": 542.63, "end": 543.17, "word": " ููู", "probability": 0.85791015625}, {"start": 543.17, "end": 543.45, "word": " ูู", "probability": 0.8896484375}, {"start": 543.45, "end": 543.65, "word": " ูู
ุง", "probability": 0.674560546875}, {"start": 543.65, "end": 544.11, "word": " ุชุญูู", "probability": 0.802001953125}, {"start": 544.11, "end": 544.53, "word": " ู
ุซูุง", "probability": 0.8525390625}, {"start": 544.53, "end": 545.17, "word": " ู
ุงูุงููุด", "probability": 0.8409423828125}, {"start": 545.17, "end": 545.45, "word": " ูุฏููุฉ", "probability": 0.86083984375}, {"start": 545.45, "end": 545.69, "word": " ูููู
", "probability": 0.806884765625}, {"start": 545.69, "end": 546.01, "word": " positive", "probability": 0.95556640625}, {"start": 546.01, "end": 546.23, "word": " ููุง", "probability": 0.372802734375}, {"start": 546.23, "end": 546.77, "word": " ู
ุงููุชุด", "probability": 0.7757568359375}, {"start": 546.77, "end": 547.49, "word": " increasing", "probability": 0.6904296875}, {"start": 547.49, "end": 548.43, "word": " ู
ุงููุชุด", "probability": 0.80023193359375}, {"start": 548.43, "end": 548.81, "word": " decreasing", "probability": 0.94189453125}, {"start": 548.81, "end": 549.15, "word": " ูุงูุช", "probability": 0.770751953125}, {"start": 549.15, "end": 549.65, "word": " increasing", "probability": 0.98583984375}], "temperature": 1.0}, {"id": 24, "seek": 57077, "start": 549.87, "end": 570.77, "text": "ูู ูุฐุง ูุคุฏู ุฅูููุง divergeุ ูุฃุ ูุง ูุคุฏู ุฅูููุง divergeุ ูุงุฒู
ุฅููุ ุงูุชูุงุช ุดุฑูุท ุชุชุญููุ ุจุชููู ุงู alternating series ุชุจุน ุชููู convergeุ ุฅุฐุง ูู
ูุชุญูู ู
ู ูุงุญุฏ ู
ู ุงูุดุฑูุทุ ูุง ูุคุฏู ุฅู ุงู series divergeุ ูุงุฒู
ููุฌุฃ ุฅูู test ุขุฎุฑุ ููู ูุงุญุธูุง ุฅุฐุง ูุงู ูุฐุง ุงูุดุฑุท ุงููู ุงููู ุจ UN ุฅู ุงู limit ููุง ูุง ูุณุงูู 0", "tokens": [3224, 1211, 23758, 7251, 33604, 16254, 11933, 20292, 11296, 18558, 432, 22807, 5296, 10721, 12399, 20193, 7251, 33604, 16254, 11933, 20292, 11296, 18558, 432, 12399, 5296, 31377, 2304, 11933, 1829, 3224, 22807, 16712, 1211, 9307, 13412, 32887, 9566, 6055, 2655, 5016, 4587, 4587, 12399, 39894, 30544, 2423, 40062, 2638, 6055, 3555, 3615, 6055, 30544, 41881, 12399, 11933, 15730, 32767, 7251, 2655, 5016, 4587, 4587, 9154, 36764, 24401, 9154, 25124, 32887, 9566, 12399, 20193, 7251, 33604, 16254, 36145, 2423, 2638, 18558, 432, 12399, 5296, 31377, 2304, 8717, 1211, 7435, 10721, 30731, 1500, 19753, 34740, 12399, 35525, 2407, 20193, 5016, 19913, 8315, 11933, 15730, 25961, 23758, 25124, 2288, 9566, 13672, 1829, 16472, 5172, 4587, 4724, 8229, 36145, 2423, 4948, 5296, 11296, 20193, 7251, 3794, 995, 45865, 1958], "avg_logprob": -0.2958829263373027, "compression_ratio": 1.8225806451612903, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 549.87, "end": 550.17, "word": "ูู", "probability": 0.872314453125}, {"start": 550.17, "end": 550.31, "word": " ูุฐุง", "probability": 0.338134765625}, {"start": 550.31, "end": 550.59, "word": " ูุคุฏู", "probability": 0.7599283854166666}, {"start": 550.59, "end": 550.77, "word": " ุฅูููุง", "probability": 0.5746256510416666}, {"start": 550.77, "end": 551.25, "word": " divergeุ", "probability": 0.584716796875}, {"start": 551.25, "end": 551.63, "word": " ูุฃุ", "probability": 0.5442708333333334}, {"start": 551.63, "end": 551.71, "word": " ูุง", "probability": 0.49462890625}, {"start": 551.71, "end": 552.03, "word": " ูุคุฏู", "probability": 0.9265950520833334}, {"start": 552.03, "end": 552.33, "word": " ุฅูููุง", "probability": 0.89892578125}, {"start": 552.33, "end": 553.47, "word": " divergeุ", "probability": 0.651611328125}, {"start": 553.47, "end": 554.05, "word": " ูุงุฒู
", "probability": 0.7996419270833334}, {"start": 554.05, "end": 554.33, "word": " ุฅููุ", "probability": 0.7486572265625}, {"start": 554.33, "end": 554.71, "word": " ุงูุชูุงุช", "probability": 0.8487955729166666}, {"start": 554.71, "end": 554.93, "word": " ุดุฑูุท", "probability": 0.7537434895833334}, {"start": 554.93, "end": 555.73, "word": " ุชุชุญููุ", "probability": 0.9281412760416666}, {"start": 555.73, "end": 556.07, "word": " ุจุชููู", "probability": 0.6046142578125}, {"start": 556.07, "end": 556.21, "word": " ุงู", "probability": 0.78076171875}, {"start": 556.21, "end": 556.77, "word": " alternating", "probability": 0.0755615234375}, {"start": 556.77, "end": 557.19, "word": " series", "probability": 0.9091796875}, {"start": 557.19, "end": 557.41, "word": " ุชุจุน", "probability": 0.5968424479166666}, {"start": 557.41, "end": 557.75, "word": " ุชููู", "probability": 0.84716796875}, {"start": 557.75, "end": 558.29, "word": " convergeุ", "probability": 0.3037109375}, {"start": 558.29, "end": 558.53, "word": " ุฅุฐุง", "probability": 0.974609375}, {"start": 558.53, "end": 558.67, "word": " ูู
", "probability": 0.95751953125}, {"start": 558.67, "end": 559.19, "word": " ูุชุญูู", "probability": 0.99072265625}, {"start": 559.19, "end": 559.37, "word": " ู
ู", "probability": 0.96142578125}, {"start": 559.37, "end": 560.33, "word": " ูุงุญุฏ", "probability": 0.947998046875}, {"start": 560.33, "end": 560.49, "word": " ู
ู", "probability": 0.9873046875}, {"start": 560.49, "end": 560.95, "word": " ุงูุดุฑูุทุ", "probability": 0.921142578125}, {"start": 560.95, "end": 561.03, "word": " ูุง", "probability": 0.79833984375}, {"start": 561.03, "end": 561.39, "word": " ูุคุฏู", "probability": 0.9368489583333334}, {"start": 561.39, "end": 561.53, "word": " ุฅู", "probability": 0.53662109375}, {"start": 561.53, "end": 561.67, "word": " ุงู", "probability": 0.7529296875}, {"start": 561.67, "end": 561.93, "word": " series", "probability": 0.90771484375}, {"start": 561.93, "end": 562.89, "word": " divergeุ", "probability": 0.6683756510416666}, {"start": 562.89, "end": 563.11, "word": " ูุงุฒู
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ุนูุงู ุฃู ูุฐุง ู
ุซูุง ุงู limit ูู ูุงุญุฏ ูุนูู ุงู series ูุฐู ุงููู ุฌูุง ูู ุงู end term ุจูููู ุงู limit ููุง ู
ูุฌุจ ุฃู ุณุงูุจ ูุงุญุฏ ูุจุงูุชุงูู ุงู limit ูุง ูุณุงูู ูุงุญุฏ ุฅุฐุง ู
ู ุงู end term ุชุณุจุจ ุงู series diverged ููู ุฅุฐุง ูุงู ุทูุนุช increasing ูุง ูุคุฏู ุฅูู ุงู series diverged ุฅุฐุง ูุงู ู
ุด ูู ุงู term positive ูุง ูุคุฏู ุฅูู ุงู series diverged ูุงุฒู
ูุนู
ู ุชุซูุงูุฉ ุฅุฐุง ูุงู ูุฐุง ุงูุดุฑุท ููุฏ ููู ุจุงู end .. ุฅุฐุง ุงู limit ูู ุงููู ู
ุด ู
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ุด", "probability": 0.9814453125}, {"start": 598.86, "end": 599.32, "word": " ู
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ูู
ุฌุฏุง ุงูู ุงุญูุง ุงููุญุธุฉ ู
ูู
ุฌุฏุง ูุฏููุฉ ุงูุชูุงุชุฉ ูุธุฑูุงุช ุงู two definitions ููุธุฑูุฉ ุงุฐุง ูุงู ุจูุง ูุดูู ููุน ุงู convergence ุชุจุนุช ุงู alternating series ุจูุฑูุญ ุจูุนู
ู ุงููู ูู series ุนูู ุงู positive terms ุงุฐุง ูุงูุช converge ุจุชููู ุงู series converge absolutely ูู ุทูุนุช diverge", "tokens": [37746, 6027, 39184, 5751, 332, 9279, 13934, 413, 1837, 432, 4724, 1829, 3794, 6156, 3224, 15730, 9673, 16095, 10874, 28259, 16472, 3224, 1975, 5016, 8315, 13672, 5016, 19913, 3660, 3714, 16095, 10874, 28259, 8032, 3215, 12610, 3660, 16712, 1211, 9307, 3660, 8717, 19913, 16572, 9307, 1975, 2407, 732, 21988, 4032, 1863, 19913, 2288, 10632, 1975, 15730, 25961, 4724, 8315, 8717, 8592, 38688, 8717, 45367, 2423, 32181, 6055, 3555, 34268, 2423, 40062, 2638, 44945, 32887, 5016, 44945, 25957, 1211, 13672, 1829, 31439, 2638, 15844, 2423, 3353, 2115, 1975, 15730, 25961, 2655, 41881, 39894, 30544, 2423, 2638, 41881, 3122, 45164, 23032, 1211, 34268, 18558, 432], "avg_logprob": -0.3131009558072457, "compression_ratio": 1.6666666666666667, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 599.58, "end": 600.12, "word": "ูุจุงูู", "probability": 0.5751953125}, {"start": 600.12, "end": 600.52, "word": " Interim", "probability": 0.228515625}, {"start": 600.52, "end": 600.72, "word": " Test", "probability": 0.427978515625}, {"start": 600.72, "end": 601.2, "word": " Series", "probability": 0.90380859375}, {"start": 601.2, "end": 602.9, "word": " Diverge", "probability": 0.62353515625}, {"start": 602.9, "end": 603.76, "word": " ุจูุณ", "probability": 0.4664306640625}, {"start": 603.76, "end": 604.06, "word": " ููุฐุง", "probability": 0.8645833333333334}, {"start": 604.06, "end": 605.4, "word": " ุงูู
ูู
", "probability": 0.8466796875}, {"start": 605.4, "end": 605.86, "word": " ุฌุฏุง", "probability": 0.95703125}, {"start": 605.86, "end": 606.14, "word": " ุงูู", "probability": 0.4609375}, {"start": 606.14, "end": 606.38, "word": " ุงุญูุง", "probability": 0.876953125}, {"start": 606.38, "end": 607.24, "word": " ุงููุญุธุฉ", "probability": 0.750732421875}, {"start": 607.24, "end": 607.52, "word": " ู
ูู
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ู", "probability": 0.9228515625}, {"start": 618.58, "end": 618.78, "word": " ุงููู", "probability": 0.698486328125}, {"start": 618.78, "end": 618.96, "word": " ูู", "probability": 0.98095703125}, {"start": 618.96, "end": 619.36, "word": " series", "probability": 0.77490234375}, {"start": 619.36, "end": 619.62, "word": " ุนูู", "probability": 0.81640625}, {"start": 619.62, "end": 619.86, "word": " ุงู", "probability": 0.75732421875}, {"start": 619.86, "end": 620.34, "word": " positive", "probability": 0.9326171875}, {"start": 620.34, "end": 621.22, "word": " terms", "probability": 0.90771484375}, {"start": 621.22, "end": 621.76, "word": " ุงุฐุง", "probability": 0.852294921875}, {"start": 621.76, "end": 622.04, "word": " ูุงูุช", "probability": 0.984130859375}, {"start": 622.04, "end": 622.38, "word": " converge", "probability": 0.80126953125}, {"start": 622.38, "end": 622.72, "word": " ุจุชููู", "probability": 0.86376953125}, {"start": 622.72, "end": 622.84, "word": " ุงู", "probability": 0.94921875}, {"start": 622.84, "end": 623.06, "word": " series", "probability": 0.93212890625}, {"start": 623.06, "end": 623.5, "word": " converge", "probability": 0.76220703125}, {"start": 623.5, "end": 624.12, "word": " absolutely", "probability": 0.5107421875}, {"start": 624.12, "end": 624.66, "word": " ูู", "probability": 0.90673828125}, {"start": 624.66, "end": 625.04, "word": " ุทูุนุช", "probability": 0.9510091145833334}, {"start": 625.04, "end": 625.76, "word": " diverge", "probability": 0.732666015625}], "temperature": 1.0}, {"id": 27, "seek": 65120, "start": 625.86, "end": 651.2, "text": "ุจุญูู ุงูุชูุงุช ุดุฑูุท ุฅุฐุง ูุงูุช ุชุญูู ุงูุชูุงุช ุดุฑูุท ุจุชููู ุงู series converge conditionally ูุง ูุคุฏู ุฅุฐุง ูุงู ุงู series converge ูุง ูุคุฏู ุฅู ุงู series diverge ุฅุฐุง ูุงูุช ุงู absolute value diverge ูุง ูุคุฏู ุฅู ุงู series diverge ุฅุฐุง ูุงูุช ุงู series converge ูุคุฏู ุฅููุง converge absolutely ุฅุฐุง ูุงูุช ุงู series diverge ุจุฑูุญุญูู ุงูุชูุงุช ุดุฑูุท ูุฅุฐุง ุชุญูู ุงูุชูุงุช ุดุฑูุท ุจุชููู converge conditionally", "tokens": [3555, 5016, 4587, 4587, 16712, 1211, 9307, 13412, 32887, 9566, 11933, 15730, 25961, 2655, 6055, 5016, 4587, 4587, 16712, 1211, 9307, 13412, 32887, 9566, 39894, 30544, 2423, 2638, 41881, 4188, 379, 20193, 7251, 33604, 16254, 11933, 15730, 25961, 2423, 2638, 41881, 20193, 7251, 33604, 16254, 36145, 2423, 2638, 18558, 432, 11933, 15730, 25961, 2655, 2423, 8236, 2158, 18558, 432, 20193, 7251, 33604, 16254, 36145, 2423, 2638, 18558, 432, 11933, 15730, 25961, 2655, 2423, 2638, 41881, 7251, 33604, 16254, 36145, 11296, 41881, 3122, 11933, 15730, 25961, 2655, 2423, 2638, 18558, 432, 4724, 32887, 5016, 5016, 4587, 4587, 16712, 1211, 9307, 13412, 32887, 9566, 4032, 28814, 15730, 6055, 5016, 4587, 4587, 16712, 1211, 9307, 13412, 32887, 9566, 39894, 30544, 41881, 4188, 379], "avg_logprob": -0.24560951004343584, "compression_ratio": 2.9485714285714284, "no_speech_prob": 2.980232238769531e-07, "words": 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"probability": 0.65185546875}, {"start": 630.74, "end": 633.44, "word": " conditionally", "probability": 0.804443359375}, {"start": 633.44, "end": 633.86, "word": " ูุง", "probability": 0.0859375}, {"start": 633.86, "end": 634.26, "word": " ูุคุฏู", "probability": 0.8414713541666666}, {"start": 634.26, "end": 634.8, "word": " ุฅุฐุง", "probability": 0.7449951171875}, {"start": 634.8, "end": 635.04, "word": " ูุงู", "probability": 0.96728515625}, {"start": 635.04, "end": 635.62, "word": " ุงู", "probability": 0.420166015625}, {"start": 635.62, "end": 635.84, "word": " series", "probability": 0.5849609375}, {"start": 635.84, "end": 635.86, "word": " converge", "probability": 0.57177734375}, {"start": 635.86, "end": 636.02, "word": " ูุง", "probability": 0.37890625}, {"start": 636.02, "end": 636.36, "word": " ูุคุฏู", "probability": 0.9378255208333334}, {"start": 636.36, "end": 636.48, "word": " ุฅู", "probability": 0.3779296875}, {"start": 636.48, "end": 636.6, "word": " ุงู", "probability": 0.884765625}, {"start": 636.6, "end": 636.84, "word": " series", "probability": 0.88330078125}, {"start": 636.84, "end": 638.08, "word": " diverge", "probability": 0.5997314453125}, {"start": 638.08, "end": 638.6, "word": " ุฅุฐุง", "probability": 0.92822265625}, {"start": 638.6, "end": 638.94, "word": " ูุงูุช", "probability": 0.7064208984375}, {"start": 638.94, "end": 639.12, "word": " ุงู", "probability": 0.865234375}, {"start": 639.12, "end": 639.4, "word": " absolute", "probability": 0.92138671875}, {"start": 639.4, "end": 639.76, "word": " value", "probability": 0.97998046875}, {"start": 639.76, "end": 640.46, "word": " diverge", "probability": 0.6251220703125}, {"start": 640.46, "end": 640.6, "word": " ูุง", "probability": 0.82080078125}, {"start": 640.6, "end": 640.9, "word": " ูุคุฏู", "probability": 0.9537760416666666}, {"start": 640.9, "end": 641.04, "word": " ุฅู", "probability": 0.91943359375}, {"start": 641.04, "end": 641.16, "word": " ุงู", "probability": 0.943359375}, {"start": 641.16, "end": 641.36, "word": " series", "probability": 0.9140625}, {"start": 641.36, "end": 642.24, "word": " diverge", "probability": 0.82177734375}, {"start": 642.24, "end": 642.72, "word": " ุฅุฐุง", "probability": 0.975341796875}, {"start": 642.72, "end": 643.02, "word": " ูุงูุช", "probability": 0.72314453125}, {"start": 643.02, "end": 643.02, "word": " ุงู", "probability": 0.716796875}, {"start": 643.02, "end": 643.02, "word": " series", "probability": 0.67724609375}, {"start": 643.02, "end": 643.36, "word": " converge", "probability": 0.966796875}, {"start": 643.36, "end": 643.68, "word": " ูุคุฏู", "probability": 0.9088541666666666}, {"start": 643.68, "end": 643.88, "word": " ุฅููุง", "probability": 0.67041015625}, {"start": 643.88, "end": 644.26, "word": " converge", "probability": 0.90771484375}, {"start": 644.26, "end": 645.44, "word": " absolutely", "probability": 0.5478515625}, {"start": 645.44, "end": 646.0, "word": " ุฅุฐุง", "probability": 0.94677734375}, {"start": 646.0, "end": 646.3, "word": " ูุงูุช", "probability": 0.9853515625}, {"start": 646.3, "end": 646.34, "word": " ุงู", "probability": 0.8857421875}, {"start": 646.34, "end": 646.34, "word": " series", "probability": 0.81787109375}, {"start": 646.34, "end": 646.68, "word": " diverge", "probability": 0.855224609375}, {"start": 646.68, "end": 647.24, "word": " ุจุฑูุญุญูู", "probability": 0.8209635416666666}, {"start": 647.24, "end": 647.56, "word": " ุงูุชูุงุช", "probability": 0.9778645833333334}, {"start": 647.56, "end": 647.94, "word": " ุดุฑูุท", "probability": 0.9895833333333334}, {"start": 647.94, "end": 648.64, "word": " ูุฅุฐุง", "probability": 0.8836263020833334}, {"start": 648.64, "end": 649.04, "word": " ุชุญูู", "probability": 0.964111328125}, {"start": 649.04, "end": 649.32, "word": " ุงูุชูุงุช", "probability": 0.9375}, {"start": 649.32, "end": 649.54, "word": " ุดุฑูุท", "probability": 0.9928385416666666}, {"start": 649.54, "end": 649.86, "word": " ุจุชููู", "probability": 0.811767578125}, {"start": 649.86, "end": 650.36, "word": " converge", "probability": 0.88134765625}, {"start": 650.36, "end": 651.2, "word": " conditionally", "probability": 0.9345703125}], "temperature": 1.0}, {"id": 28, "seek": 66374, "start": 652.24, "end": 663.74, "text": "ูุงููุธุฑูุฉ ุฏู ู
ูู
ุฉ ุฅุฐุง ูุงูุช ุงู summation ุนูู ุงู a n converge ุนูู ุงู absolute value converge ูุจุงูุชุงูู ูุงุฒู
ุงูุดุฑูุท ุงูุชูุงุชุฉ ูููููุง ู
ุชุญูููู ูุฅูู ุฃุตูุง ุงู series ุนูู a n ุจุชููู converge", "tokens": [2407, 6027, 1863, 19913, 2288, 10632, 11778, 1829, 3714, 16095, 3660, 11933, 15730, 25961, 2655, 2423, 28811, 15844, 2423, 257, 297, 41881, 15844, 2423, 8236, 2158, 41881, 6156, 3555, 6027, 2655, 6027, 1829, 5296, 31377, 2304, 25124, 32887, 9566, 16712, 1211, 9307, 3660, 7251, 30544, 14407, 44650, 5016, 4587, 4587, 9957, 5296, 28814, 1863, 3224, 5551, 9381, 15040, 2423, 2638, 15844, 257, 297, 39894, 30544, 41881], "avg_logprob": -0.21805037802724697, "compression_ratio": 1.5317919075144508, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 652.24, "end": 652.82, "word": "ูุงููุธุฑูุฉ", "probability": 0.8557535807291666}, {"start": 652.82, "end": 653.02, "word": " ุฏู", "probability": 0.53546142578125}, {"start": 653.02, "end": 653.54, "word": " ู
ูู
ุฉ", "probability": 0.98828125}, {"start": 653.54, "end": 653.76, "word": " ุฅุฐุง", "probability": 0.837646484375}, {"start": 653.76, "end": 654.06, "word": " ูุงูุช", "probability": 0.95458984375}, {"start": 654.06, "end": 654.14, "word": " ุงู", "probability": 0.427001953125}, {"start": 654.14, "end": 654.46, "word": " summation", "probability": 0.8046875}, {"start": 654.46, "end": 654.68, "word": " ุนูู", "probability": 0.55712890625}, {"start": 654.68, "end": 654.78, "word": " ุงู", "probability": 0.70263671875}, {"start": 654.78, "end": 654.84, "word": " a", "probability": 0.1854248046875}, {"start": 654.84, "end": 654.98, "word": " n", "probability": 0.274169921875}, {"start": 654.98, "end": 655.5, "word": " converge", "probability": 0.451171875}, {"start": 655.5, "end": 655.72, "word": " ุนูู", "probability": 0.72607421875}, {"start": 655.72, "end": 655.8, "word": " ุงู", "probability": 0.70947265625}, {"start": 655.8, "end": 656.1, "word": " absolute", "probability": 0.935546875}, {"start": 656.1, "end": 656.4, "word": " value", "probability": 0.98046875}, {"start": 656.4, "end": 656.96, "word": " converge", "probability": 0.67919921875}, {"start": 656.96, "end": 658.24, "word": " ูุจุงูุชุงูู", "probability": 0.9341634114583334}, {"start": 658.24, "end": 658.92, "word": " ูุงุฒู
", "probability": 0.9796549479166666}, {"start": 658.92, "end": 659.28, "word": " ุงูุดุฑูุท", "probability": 0.8919270833333334}, {"start": 659.28, "end": 659.68, "word": " ุงูุชูุงุชุฉ", "probability": 0.9012451171875}, {"start": 659.68, "end": 660.02, "word": " ูููููุง", "probability": 0.9617513020833334}, {"start": 660.02, "end": 660.98, "word": " ู
ุชุญูููู", "probability": 0.9794921875}, {"start": 660.98, "end": 662.12, "word": " ูุฅูู", "probability": 0.7830810546875}, {"start": 662.12, "end": 662.34, "word": " ุฃุตูุง", "probability": 0.8997395833333334}, {"start": 662.34, "end": 662.48, "word": " ุงู", "probability": 0.9609375}, {"start": 662.48, "end": 662.76, "word": " series", "probability": 0.93798828125}, {"start": 662.76, "end": 662.94, "word": " ุนูู", "probability": 0.48193359375}, {"start": 662.94, "end": 663.04, "word": " a", "probability": 0.83056640625}, {"start": 663.04, "end": 663.14, "word": " n", "probability": 0.9033203125}, {"start": 663.14, "end": 663.42, "word": " ุจุชููู", "probability": 0.83056640625}, {"start": 663.42, "end": 663.74, "word": " converge", "probability": 0.861328125}], "temperature": 1.0}, {"id": 29, "seek": 68521, "start": 664.67, "end": 685.21, "text": "ูุดูู ุงูุฃู
ุซูุฉ ุงูู Alternating Harmonic Series ูุงูุต ูุงุญุฏ ุฃูุณ N ุฒุงุฆุฏ ูุงุญุฏ ูู ูุงุญุฏ ุนูู N ูุฃู ูู ุดูููุง ูุฐู ุจูุธู ุงู summation ูุงุญุฏ ุนูู N ูู ุงู harmonic series ุงููู ุงุญูุง ุจูุนุฑููุง ููู ูู ุถููุง ุนูููุง ุงูู
ูุฌุจ ูุงูุณุงูุจ ุจูุณู
ููุง ุงู alternating harmonic series ุงููู ูู ูุงุญุฏ ูุงูุต ูุต ุฒุงุฆุฏ ุชูุช ูุงูุต ุฑุจุน ุฅูู ุฃูู", "tokens": [1863, 8592, 38688, 16247, 2304, 12984, 37977, 2423, 39184, 23830, 990, 40599, 299, 13934, 8717, 995, 4587, 9381, 36764, 24401, 5551, 10859, 3794, 426, 30767, 16373, 3215, 36764, 24401, 8978, 36764, 24401, 15844, 426, 5296, 33456, 45164, 13412, 26895, 8315, 29538, 4724, 1829, 19913, 1211, 2423, 28811, 36764, 24401, 15844, 426, 39896, 2423, 32270, 2638, 13672, 1829, 1975, 5016, 8315, 44945, 3615, 28480, 11296, 44381, 45164, 48812, 5172, 8315, 25894, 11296, 9673, 29245, 3555, 16070, 3794, 6027, 3555, 44945, 38251, 1829, 11296, 2423, 40062, 32270, 2638, 13672, 1829, 39896, 36764, 24401, 8717, 995, 4587, 9381, 8717, 9381, 30767, 16373, 3215, 6055, 1211, 2655, 8717, 995, 4587, 9381, 12602, 3555, 3615, 30731, 5551, 4587, 1211], "avg_logprob": -0.25557065217391306, "compression_ratio": 1.8360655737704918, "no_speech_prob": 5.960464477539062e-07, "words": [{"start": 664.67, "end": 665.05, "word": "ูุดูู", "probability": 0.7801106770833334}, {"start": 665.05, "end": 665.65, "word": " ุงูุฃู
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ููุง", "probability": 0.904541015625}, {"start": 680.75, "end": 680.87, "word": " ุงู", "probability": 0.873046875}, {"start": 680.87, "end": 681.43, "word": " alternating", "probability": 0.810546875}, {"start": 681.43, "end": 682.01, "word": " harmonic", "probability": 0.83544921875}, {"start": 682.01, "end": 682.39, "word": " series", "probability": 0.900390625}, {"start": 682.39, "end": 682.61, "word": " ุงููู", "probability": 0.788330078125}, {"start": 682.61, "end": 682.77, "word": " ูู", "probability": 0.689453125}, {"start": 682.77, "end": 683.07, "word": " ูุงุญุฏ", "probability": 0.947509765625}, {"start": 683.07, "end": 683.39, "word": " ูุงูุต", "probability": 0.975830078125}, {"start": 683.39, "end": 683.59, "word": " ูุต", "probability": 0.6356201171875}, {"start": 683.59, "end": 683.85, "word": " ุฒุงุฆุฏ", "probability": 0.8899739583333334}, {"start": 683.85, "end": 684.09, "word": " ุชูุช", "probability": 0.73046875}, {"start": 684.09, "end": 684.39, "word": " ูุงูุต", "probability": 0.981689453125}, {"start": 684.39, "end": 684.71, "word": " ุฑุจุน", "probability": 0.9529622395833334}, {"start": 684.71, "end": 684.87, "word": " ุฅูู", "probability": 0.8486328125}, {"start": 684.87, "end": 685.21, "word": " ุฃูู", "probability": 0.712158203125}], "temperature": 1.0}, {"id": 30, "seek": 70294, "start": 685.78, "end": 702.94, "text": "ุงูุงู ูุงุฏ ุงู series ุจูุดูููุง ูู ูู converge ููุง diverge ุทุจุนุง ุงู harmonic series ูุญุงููุง ุจุฏูู ููุต ูุงุญุฏ ุฃุณุฆู ูุงูุช diverge ุงููู ููู series ูููู ุชุณุงูู ูุงุญุฏ ูุงูุช diverge ุทุจ ูุดูู ุงู alternating ูู ุชุฎุชูู ููุง ูุฃ ุงูุงู ูู ุฃุฌููุง ุทุจุนุง ุงูุญูู ุงูุชูู ุดุฑูุท ุชุจุนุชูุง", "tokens": [6027, 7649, 8032, 18513, 2423, 2638, 4724, 1863, 8592, 38688, 11296, 8032, 1211, 39896, 41881, 49429, 18558, 432, 23032, 3555, 3615, 995, 2423, 32270, 2638, 5296, 5016, 6027, 11296, 47525, 11536, 8717, 4587, 9381, 36764, 24401, 5551, 3794, 19986, 1211, 25961, 2655, 18558, 432, 13672, 1829, 8978, 3224, 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"probability": 0.687744140625}, {"start": 702.14, "end": 702.46, "word": " ุดุฑูุท", "probability": 0.923828125}, {"start": 702.46, "end": 702.94, "word": " ุชุจุนุชูุง", "probability": 0.853271484375}], "temperature": 1.0}, {"id": 31, "seek": 72688, "start": 704.72, "end": 726.88, "text": "UN ุชุณุงูู 1 ุนูู N ู N ุฃูุจุฑ ุฃู ูุณุงูู ูุงุญุฏ ุงููู ูู ุงู UN ุฃููุง ุงู 1 ุนูู N ู
ูุฌุจุฉ ุจุนุฏูู ุงูู
ุดุชูุฉ ููุต 1 ุนูู N ุชุฑุจูู ุณุงูู ู ุชููู decreasing limit ุงู UN ูุณุงูู limit ุงู 1 ุนูู N ูุณุงูู ุณูุฑ ุฅุฐุง ุงู series ุชุจุนุชูุง converge ุฅุฐุง ูุญุธุฉ ุงู alternating harmonic series ู
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ุงุดู ุจููููู converge ู
ุงูุงูููุด ููุน ุงู convergence ูู
ุง ููููู converge ู ุฎูุงุต ุงุญูู ุงุชูุช ุดูุฑู ู
ุจุงุดุฑุฉ ู ุงุชูุช ุฎูุงุต ุจุฏูู absolute value ููู ูู ูุงููู ุดูู ุงู series converge ุงูุด ููุน ุงู convergence ุชุจุนูุง ุจุฑูุญ ุจุนู
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ูุฌุจุฉ UN' ุณุงูู ูุงูุต ูุงุญุฏ ุนูู ุงุชููู ุงูุฌุฏุฑุณ ุณุงูุจุฉ ูุจุงูุชุงูู ุงู UN decreasing limit ุงููุงุญุฏ ุนูู ุงูุฌุฏุฑุณ ุงูุงุฑุจุน ูุณุงูู ูุงุญุฏ ุนู
ุงูุงูููุง ุงููู ูู ุณูุฑุ ุฅุฐุง ุงู series ุจุฑุถู convergent ุชุณู
ูุด ูุงูุต ูุงุญุฏ ูุต ุงู ุฒุงุฆุฏ ูุงุญุฏ ูู N ุชุฑุจูู ุฒุงุฆุฏ ุฎู
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ู ุงูุณูุฑ ุทุจุนุง ู
ูุฌุจุฉ UN' ุณูู ูุงูุต ุชู
ุงููุฉ N ุนูู N ุชุฑุจูู ุฒุงุฆุฏ ูุงุญุฏ ูู ุชุฑุฌุน ุณุงูุจุฉ ูุฌูุฏ ููุง ุณุงูุจ ูุงู N ุทุจุนุง ู
ูุฌุจุฉ ูุจูู ูู decreasing ูุฃู ุงู limit ู N ุชุฑุจูู ุฒุงุฆุฏ ุฎู
ุณ ุนูู N ุชุฑุจูู ุฒุงุฆุฏ ูุงุญุฏ ุฏุฑุฌุฉ ุงู bus ุชุณุงูู ุฏุฑุฌุฉ ู
ูุงู
ุงู limit ูุณุงูู ูุงุญุฏ ูุง ูุณุงูู ุณุชุฉ ูุจุงูุชุงูู ุงู test ูู ูุฐู ุงูุญููุฉ ู
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ูุงู
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ู ุงูุดุฑูุท ูุฐู ูุงู test fail ูุง ูุฌุจ ุงู ุงูุง ุงุณุชุฎุฏู
ู ููู ุจูุณุชููุฏ ู
ู ูุฐุง ุงูุดุฑุท ุงู ุงู limit ูุง ูุณุงูู ุตูุฑ ูู ูุณุงูู ูุงุญุฏ ูุจูู ุงู limit ุจุฑูุญ ุจุฌูุจ ุงู limit ูู a,n ูุฐู ูููุง ุงูุงู ุจุงุณุชุฎุฏุงู
ุงู interim test limit ูุงูุต ูุงุญุฏ ูุต n ุฒุงุฆุฏ ูุงุญุฏ ูู n ุชุฑุจูู ุฒุงุฆุฏ ุฎู
ุณ ุนูู n ุชุฑุจูู ุฒุงุฆุฏ ูุงุญุฏ ูุณุงูู ู
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ู ูุงุญุฏ ุงู series divers ููุณุช ู
ู ููุฏุฑ ูุฐุง ุงูุดุฑุท ูุฅูู
ุง ุจุงู end term test ุทุจุนุง ููุง ูู ู
ูุงุญุธุฉ ุฃูู ูู
ูู ุงุณุชุฎุฏุงู
ุงู end term test ู
ุจุงุดุฑุฉ ูุนูู ูู ุฃูุง ูุงุญุธุช ู
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ุด ุณูุฑ ู
ุด ุถุฑูุฑู ุฃุนู
ู ูุฐู ูููุง ุนูู ุทูู ุจุนู
ู ุจุงู end term test ู ุจุทูุนูุง divers ููุฐุง ู
ุด ุถุฑูุฑู ููู ูู ุฃูุง ุฑูุญุช ุนู
ูุช ุงูุดุฑูุท ุฒู ูููุฏู ูู
ุงูุงุญุชุด ูุฐู ุงูู
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ุง ูุตูุช ูููุง ุนุงุฏู ุจุนู
ู ุจุนุชูู in turn test ูุงูุงู ูู ุนูุฏู ู
ูุงุญุธุฉ ููุง ุจููู every absolutely convergent series converges ุงู convergent series absolutely ุจุชููู ูู converges however the converse statement is false", "tokens": [12610, 995, 11331, 49975, 5296, 15042, 4032, 36520, 2655, 46740, 8315, 6225, 995, 16254, 4724, 25957, 1211, 4724, 34268, 4587, 1211, 294, 1261, 1500, 6156, 6027, 7649, 8978, 18871, 16254, 3714, 15040, 5016, 19913, 3660, 34105, 4724, 39648, 633, 3122, 9652, 6930, 2638, 9652, 2880, 1975, 1829, 9652, 6930, 2638, 3122, 39894, 30544, 8032, 7578, 9652, 2880, 4461, 264, 416, 4308, 5629, 307, 7908], "avg_logprob": -0.35168269230769234, "compression_ratio": 1.576271186440678, "no_speech_prob": 0.0, "words": [{"start": 852.68, "end": 853.56, "word": "ููุง", "probability": 0.423583984375}, {"start": 853.56, "end": 853.8, "word": " ุญุชู", "probability": 0.8486328125}, {"start": 853.8, "end": 854.0, "word": " ูู
ุง", "probability": 0.660400390625}, {"start": 854.0, "end": 854.36, "word": " ูุตูุช", "probability": 0.9095052083333334}, {"start": 854.36, "end": 854.66, "word": " ูููุง", "probability": 0.82177734375}, {"start": 854.66, "end": 854.96, "word": " ุนุงุฏู", "probability": 0.8297526041666666}, {"start": 854.96, "end": 855.3, "word": " ุจุนู
ู", "probability": 0.9069010416666666}, {"start": 855.3, "end": 855.78, "word": " ุจุนุชูู", "probability": 0.441986083984375}, {"start": 855.78, "end": 856.02, "word": " in", "probability": 0.1285400390625}, {"start": 856.02, "end": 856.24, "word": " turn", "probability": 0.69873046875}, {"start": 856.24, "end": 857.08, "word": " test", "probability": 0.8955078125}, {"start": 857.08, "end": 864.08, "word": " ูุงูุงู", "probability": 0.626220703125}, {"start": 864.08, "end": 864.22, "word": " ูู", "probability": 0.57861328125}, {"start": 864.22, "end": 864.64, "word": " ุนูุฏู", "probability": 0.796875}, {"start": 864.64, "end": 865.32, "word": " ู
ูุงุญุธุฉ", "probability": 0.980859375}, {"start": 865.32, "end": 865.52, "word": " ููุง", "probability": 0.8720703125}, {"start": 865.52, "end": 865.8, "word": " ุจููู", "probability": 0.841552734375}, {"start": 865.8, "end": 866.14, "word": " every", "probability": 0.1944580078125}, {"start": 866.14, "end": 867.06, "word": " absolutely", "probability": 0.6650390625}, {"start": 867.06, "end": 867.9, "word": " convergent", "probability": 0.9296875}, {"start": 867.9, "end": 868.52, "word": " series", "probability": 0.9404296875}, {"start": 868.52, "end": 869.86, "word": " converges", "probability": 0.94140625}, {"start": 869.86, "end": 870.38, "word": " ุงู", "probability": 0.54864501953125}, {"start": 870.38, "end": 872.48, "word": " convergent", "probability": 0.814697265625}, {"start": 872.48, "end": 873.22, "word": " series", "probability": 0.9462890625}, {"start": 873.22, "end": 874.08, "word": " absolutely", "probability": 0.477783203125}, {"start": 874.08, "end": 874.44, "word": " ุจุชููู", "probability": 0.93310546875}, {"start": 874.44, "end": 874.56, "word": " ูู", "probability": 0.763427734375}, {"start": 874.56, "end": 875.26, "word": " converges", "probability": 0.931640625}, {"start": 875.26, "end": 875.9, "word": " however", "probability": 0.9404296875}, {"start": 875.9, "end": 876.7, "word": " the", "probability": 0.640625}, {"start": 876.7, "end": 877.88, "word": " converse", "probability": 0.6695556640625}, {"start": 877.88, "end": 878.32, "word": " statement", "probability": 0.93994140625}, {"start": 878.32, "end": 878.64, "word": " is", "probability": 0.92041015625}, {"start": 878.64, "end": 879.06, "word": " false", "probability": 0.880859375}], "temperature": 1.0}, {"id": 38, "seek": 90331, "start": 879.29, "end": 903.31, "text": "ูุนูู ูู ูู conversion series ุจุชููู absolutely convergeุ ูุฃ ููุณุช ูู series converge ุจุชููู absolutely converge ููู ูู absolutely converge ูู converge ููุดุ ูุฃู many conversion series do not converge many conversion series do not converge absolutely ูุชูุฑ ูู ู
ู ุงู conversion series ุฒู ุงู harmonic series ูุจู ุดููุฉ ุงู harmonic series ุงููู ูู ุงูู
ุซุงู ุงูุฃูู", "tokens": [40228, 22653, 8032, 1211, 28242, 14298, 2638, 39894, 30544, 3122, 41881, 22807, 5296, 10721, 32239, 14851, 28242, 2638, 41881, 39894, 30544, 3122, 41881, 44381, 28242, 3122, 41881, 39896, 41881, 32239, 8592, 22807, 5296, 33456, 867, 14298, 2638, 360, 406, 41881, 867, 14298, 2638, 360, 406, 41881, 3122, 9122, 2655, 13546, 8978, 9154, 2423, 14298, 2638, 30767, 1829, 2423, 32270, 2638, 12174, 36150, 13412, 2407, 10632, 2423, 32270, 2638, 13672, 1829, 8978, 9673, 12984, 6027, 16247, 12610], "avg_logprob": -0.17299106600996736, "compression_ratio": 2.234375, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 879.29, "end": 879.89, "word": "ูุนูู", "probability": 0.907470703125}, {"start": 879.89, "end": 880.55, "word": " ูู", "probability": 0.845947265625}, {"start": 880.55, "end": 880.87, "word": " ูู", "probability": 0.96142578125}, {"start": 880.87, "end": 881.43, "word": " conversion", "probability": 0.420166015625}, {"start": 881.43, "end": 881.87, "word": " series", "probability": 0.83251953125}, {"start": 881.87, "end": 882.25, "word": " ุจุชููู", "probability": 0.9853515625}, {"start": 882.25, "end": 882.79, "word": " absolutely", "probability": 0.58935546875}, {"start": 882.79, "end": 883.31, "word": " convergeุ", "probability": 0.4974365234375}, {"start": 883.31, "end": 883.53, "word": " ูุฃ", "probability": 0.939453125}, {"start": 883.53, "end": 884.31, "word": " ููุณุช", "probability": 0.8095703125}, {"start": 884.31, "end": 884.57, "word": " ูู", "probability": 0.986328125}, {"start": 884.57, "end": 884.99, "word": " series", "probability": 0.90576171875}, {"start": 884.99, "end": 885.47, "word": " converge", "probability": 0.9228515625}, {"start": 885.47, "end": 885.83, "word": " ุจุชููู", "probability": 0.98583984375}, {"start": 885.83, "end": 886.35, "word": " absolutely", "probability": 0.6875}, {"start": 886.35, "end": 886.85, "word": " converge", "probability": 0.9599609375}, {"start": 886.85, "end": 887.29, "word": " ููู", "probability": 0.66015625}, {"start": 887.29, "end": 887.57, "word": " ูู", "probability": 0.9619140625}, {"start": 887.57, "end": 888.11, "word": " absolutely", "probability": 0.61181640625}, {"start": 888.11, "end": 888.63, "word": " converge", "probability": 0.9833984375}, {"start": 888.63, "end": 888.83, "word": " ูู", "probability": 0.88525390625}, {"start": 888.83, "end": 889.75, "word": " converge", "probability": 0.9208984375}, {"start": 889.75, "end": 890.25, "word": " ููุดุ", "probability": 0.8167317708333334}, {"start": 890.25, "end": 890.41, "word": " ูุฃู", "probability": 0.831298828125}, {"start": 890.41, "end": 890.71, "word": " many", "probability": 0.79931640625}, {"start": 890.71, "end": 891.37, "word": " conversion", "probability": 0.6640625}, {"start": 891.37, "end": 891.95, "word": " series", "probability": 0.947265625}, {"start": 891.95, "end": 892.33, "word": " do", "probability": 0.52783203125}, {"start": 892.33, "end": 892.55, "word": " not", "probability": 0.9658203125}, {"start": 892.55, "end": 893.13, "word": " converge", "probability": 0.9970703125}, {"start": 893.13, "end": 893.65, "word": " many", "probability": 0.34423828125}, {"start": 893.65, "end": 894.21, "word": " conversion", "probability": 0.87255859375}, {"start": 894.21, "end": 894.51, "word": " series", "probability": 0.94873046875}, {"start": 894.51, "end": 894.73, "word": " do", "probability": 0.86865234375}, {"start": 894.73, "end": 894.93, "word": " not", "probability": 0.94921875}, {"start": 894.93, "end": 895.39, "word": " converge", "probability": 0.99755859375}, {"start": 895.39, "end": 896.09, "word": " absolutely", "probability": 0.72119140625}, {"start": 896.09, "end": 896.77, "word": " ูุชูุฑ", "probability": 0.8810221354166666}, {"start": 896.77, "end": 896.91, "word": " ูู", "probability": 0.9326171875}, {"start": 896.91, "end": 897.13, "word": " ู
ู", "probability": 0.859375}, {"start": 897.13, "end": 897.41, "word": " ุงู", "probability": 0.958984375}, {"start": 897.41, "end": 898.17, "word": " conversion", "probability": 0.9091796875}, {"start": 898.17, "end": 898.55, "word": " series", "probability": 0.9443359375}, {"start": 898.55, "end": 898.77, "word": " ุฒู", "probability": 0.879638671875}, {"start": 898.77, "end": 898.87, "word": " ุงู", "probability": 0.90380859375}, {"start": 898.87, "end": 899.17, "word": " harmonic", "probability": 0.90185546875}, {"start": 899.17, "end": 899.51, "word": " series", "probability": 0.93115234375}, {"start": 899.51, "end": 899.73, "word": " ูุจู", "probability": 0.973388671875}, {"start": 899.73, "end": 900.17, "word": " ุดููุฉ", "probability": 0.8855794270833334}, {"start": 900.17, "end": 900.61, "word": " ุงู", "probability": 0.7646484375}, {"start": 900.61, "end": 900.91, "word": " harmonic", "probability": 0.9365234375}, {"start": 900.91, "end": 901.43, "word": " series", "probability": 0.9404296875}, {"start": 901.43, "end": 902.19, "word": " ุงููู", "probability": 0.75439453125}, {"start": 902.19, "end": 902.31, "word": " ูู", "probability": 0.93017578125}, {"start": 902.31, "end": 902.91, "word": " ุงูู
ุซุงู", "probability": 0.9622395833333334}, {"start": 902.91, "end": 903.31, "word": " ุงูุฃูู", "probability": 0.93017578125}], "temperature": 1.0}, {"id": 39, "seek": 92938, "start": 903.64, "end": 929.38, "text": "ูู
ุง converge ุชูุนุจุช ูู converge ููู absolutely ูู ุงู harmonic seeded ุจุชููู die verge ุงููู ูู ูู ุงู metaretherapy ุงููู
ู ุฃู
ุซูุฉ example ุฃุฑุจุนุฉ ุตู
ูุด ุงูููุต ูุงุญุฏ ุฃุณุฆูุฉ ูุงุญุฏ ูู ูุงุญุฏ ุนูู n ุชุฑุจูุฉ ุงูุดูู ูู ูู converge absolutely ููุง conditional ุทุจุนุง ุงูุฃุณุฆูุฉ ูุฐู ูููุง ุนูู ุงู .. ููุง ุจุฏูุง ููุชุจ ููุง ุงูู converge ูุดูู absolutely ุงู conditional", "tokens": [3224, 15042, 41881, 6055, 1211, 3615, 3555, 2655, 39896, 41881, 44381, 3122, 39896, 2423, 32270, 8871, 292, 39894, 30544, 978, 37164, 13672, 1829, 39896, 8978, 2423, 1131, 11298, 511, 569, 88, 16472, 24793, 1211, 5551, 2304, 12984, 37977, 1365, 5551, 25513, 27884, 20328, 2304, 1829, 8592, 28239, 4587, 9381, 36764, 24401, 5551, 3794, 19986, 37977, 36764, 24401, 8978, 36764, 24401, 15844, 297, 6055, 2288, 21292, 3660, 16472, 8592, 38688, 8032, 1211, 39896, 41881, 3122, 49429, 27708, 23032, 3555, 3615, 995, 16247, 3794, 19986, 37977, 29538, 28242, 11296, 15844, 2423, 4386, 34105, 47525, 8315, 8717, 4117, 2655, 3555, 34105, 16472, 3224, 41881, 8717, 8592, 38688, 3122, 1975, 2407, 27708], "avg_logprob": -0.37815367409942346, "compression_ratio": 1.789272030651341, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 903.64, "end": 904.34, "word": "ูู
ุง", "probability": 0.4190673828125}, {"start": 904.34, "end": 904.9, "word": " converge", "probability": 0.309814453125}, {"start": 904.9, "end": 906.66, "word": " ุชูุนุจุช", "probability": 0.6640625}, {"start": 906.66, "end": 906.76, "word": " ูู", "probability": 0.3662109375}, {"start": 906.76, "end": 907.34, "word": " converge", "probability": 0.86767578125}, {"start": 907.34, "end": 907.88, "word": " ููู", "probability": 0.61181640625}, {"start": 907.88, "end": 908.58, "word": " absolutely", "probability": 0.470703125}, {"start": 908.58, "end": 908.96, "word": " ูู", "probability": 0.89306640625}, {"start": 908.96, "end": 909.1, "word": " ุงู", "probability": 0.806640625}, {"start": 909.1, "end": 909.38, "word": " harmonic", "probability": 0.379150390625}, {"start": 909.38, "end": 909.72, "word": " seeded", "probability": 0.3214111328125}, {"start": 909.72, "end": 910.12, "word": " ุจุชููู", "probability": 0.962646484375}, {"start": 910.12, "end": 910.68, "word": " die", "probability": 0.17919921875}, {"start": 910.68, "end": 911.22, "word": " verge", "probability": 0.5205078125}, {"start": 911.22, "end": 912.86, "word": " ุงููู", "probability": 0.7939453125}, {"start": 912.86, "end": 913.22, "word": " ูู", "probability": 0.80029296875}, {"start": 913.22, "end": 914.06, "word": " ูู", "probability": 0.61474609375}, {"start": 914.06, "end": 914.14, "word": " ุงู", "probability": 0.556640625}, {"start": 914.14, "end": 915.04, "word": " metaretherapy", "probability": 0.3557861328125}, {"start": 915.04, "end": 915.6, "word": " ุงููู
ู", "probability": 0.7786458333333334}, {"start": 915.6, "end": 916.04, "word": " ุฃู
ุซูุฉ", "probability": 0.92529296875}, {"start": 916.04, "end": 916.96, "word": " example", "probability": 0.84375}, {"start": 916.96, "end": 917.6, "word": " ุฃุฑุจุนุฉ", "probability": 0.6886393229166666}, {"start": 917.6, "end": 918.96, "word": " ุตู
ูุด", "probability": 0.66522216796875}, {"start": 918.96, "end": 919.28, "word": " ุงูููุต", "probability": 0.85546875}, {"start": 919.28, "end": 919.48, "word": " ูุงุญุฏ", "probability": 0.869384765625}, {"start": 919.48, "end": 919.7, "word": " ุฃุณุฆูุฉ", "probability": 0.745361328125}, {"start": 919.7, "end": 920.06, "word": " ูุงุญุฏ", "probability": 0.77978515625}, {"start": 920.06, "end": 920.18, "word": " ูู", "probability": 0.93505859375}, {"start": 920.18, "end": 920.44, "word": " ูุงุญุฏ", "probability": 0.990966796875}, {"start": 920.44, "end": 920.62, "word": " ุนูู", "probability": 0.9013671875}, {"start": 920.62, "end": 920.88, "word": " n", "probability": 0.483154296875}, {"start": 920.88, "end": 921.52, "word": " ุชุฑุจูุฉ", "probability": 0.66790771484375}, {"start": 921.52, "end": 922.06, "word": " ุงูุดูู", "probability": 0.86572265625}, {"start": 922.06, "end": 922.22, "word": " ูู", "probability": 0.962890625}, {"start": 922.22, "end": 922.34, "word": " ูู", "probability": 0.9013671875}, {"start": 922.34, "end": 922.82, "word": " converge", "probability": 0.96533203125}, {"start": 922.82, "end": 923.46, "word": " absolutely", "probability": 0.697265625}, {"start": 923.46, "end": 923.72, "word": " ููุง", "probability": 0.77978515625}, {"start": 923.72, "end": 924.06, "word": " conditional", "probability": 0.48828125}, {"start": 924.06, "end": 924.3, "word": " ุทุจุนุง", "probability": 0.9356689453125}, {"start": 924.3, "end": 924.66, "word": " ุงูุฃุณุฆูุฉ", "probability": 0.986572265625}, {"start": 924.66, "end": 924.88, "word": " ูุฐู", "probability": 0.34326171875}, {"start": 924.88, "end": 925.44, "word": " ูููุง", "probability": 0.9921875}, {"start": 925.44, "end": 925.86, "word": " ุนูู", "probability": 0.5712890625}, {"start": 925.86, "end": 926.18, "word": " ุงู", "probability": 0.67578125}, {"start": 926.18, "end": 926.6, "word": " ..", "probability": 0.430419921875}, {"start": 926.6, "end": 926.84, "word": " ููุง", "probability": 0.896484375}, {"start": 926.84, "end": 927.12, "word": " ุจุฏูุง", "probability": 0.943603515625}, {"start": 927.12, "end": 927.36, "word": " ููุชุจ", "probability": 0.9886474609375}, {"start": 927.36, "end": 927.52, "word": " ููุง", "probability": 0.97314453125}, {"start": 927.52, "end": 927.72, "word": " ุงูู", "probability": 0.69384765625}, {"start": 927.72, "end": 928.1, "word": " converge", "probability": 0.97705078125}, {"start": 928.1, "end": 928.4, "word": " ูุดูู", "probability": 0.7930501302083334}, {"start": 928.4, "end": 928.8, "word": " absolutely", "probability": 0.60595703125}, {"start": 928.8, "end": 929.0, "word": " ุงู", "probability": 0.85009765625}, {"start": 929.0, "end": 929.38, "word": " conditional", "probability": 0.80029296875}], "temperature": 1.0}, {"id": 40, "seek": 94337, "start": 930.35, "end": 943.37, "text": "ุงูุตู
ู
ุด ุงููู Absolute ูุงู ูุณุงูู ุจูุดูู ุงููู ูุงูุต ูุงุญุฏ ูุงุซููู ุจูุธู ูุฐุง ูุงุญุฏ ุนูู ุงูุชุฑ ุจูู ุทุจุนุง ุงูุตู
ู
ุด ุงููุงุญุฏ ุนูู ุงูุชุฑ ุจูู converges ูุฅููุง ููู series P2 ุฃูุจุฑ ู
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ุฌุจูู ูููุง ุณุงูู ูุจุงูุชุงูู ุงูุด ุจูุนู
ูุ ุจูุญุท ุงู sin ุฏุงุฎู absolute valueุ ูุงุญุธูุง ุงู series ูุฐู alternating series ู
ุงููุด ูููุง ูุงูุต ูุงุญุฏ ูุต ุงูุ ููู ูููุง sin ู
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ุง ุฃุฌูุจ ุงู positive ู
ููุง ูุงุฒู
ุฃุญุท ุงู sign ุฏุงุฎู absolute value ุงูุขู ุจุฏูุง ูุดูู ุงู series of positive terms ุงููู ุตุงุฑุช ูู ูู convergent ููุง divergent ูุณุชุฎุฏู
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ุนุฑูู ุฃู ุงู absolute sign ุฃูู ุฃู ูุณูู ูุงุญุฏ ุจููุณู
ุงูุทุฑููู ุนูู N ุชุฑุจูุน ุงูุขู ุงู series ูุฐู ุงููู ูุจูุฑุฉ ูุงุฒู
ุชููู converge ุทุจุนุง ูู converge ูุฅููุง ูู series P2 ุณูุงุก ุงุชููู ุงูุจุฑ ู
ู ูุงุญุฏ ูุจุงูุชุงูู ุจุงู comparison test ุงูุตู
ุงุด ุงููู absolute ู ุงู AN convergence ุงุฐุง ุงูุตู
ุงุด ุงููู ู ุงู AN ุชุจุนุชู converge absolutely", "tokens": [6027, 20292, 31439, 2423, 9660, 1500, 23032, 3555, 3615, 995, 20449, 32887, 5172, 14739, 2423, 8236, 1465, 5551, 4587, 1211, 34051, 7251, 3794, 2407, 7578, 36764, 24401, 44945, 4587, 38251, 41950, 28480, 9957, 15844, 426, 6055, 25513, 40228, 6024, 48506, 2423, 2638, 8032, 8848, 1829, 13672, 1829, 9122, 3555, 48923, 5296, 31377, 2304, 6055, 30544, 41881, 23032, 3555, 3615, 995, 39896, 41881, 5296, 28814, 1863, 11296, 8978, 2638, 430, 17, 8608, 2407, 16606, 1975, 2655, 1863, 9957, 1975, 4117, 26890, 9154, 36764, 24401, 46599, 6027, 2655, 6027, 1829, 20666, 9660, 1500, 31767, 2304, 33599, 13672, 1829, 8236, 5296, 2423, 5252, 32181, 1975, 15730, 31767, 2304, 33599, 13672, 1829, 5296, 2423, 5252, 6055, 3555, 3615, 31371, 41881, 3122], "avg_logprob": -0.3230932084685665, "compression_ratio": 1.8066914498141264, "no_speech_prob": 1.6093254089355469e-06, "words": [{"start": 981.87, "end": 982.15, "word": "ุงููู", "probability": 0.42474365234375}, {"start": 982.15, "end": 982.33, "word": " ูู", "probability": 0.9560546875}, {"start": 982.33, "end": 982.47, "word": " ุงู", "probability": 0.7958984375}, {"start": 982.47, "end": 982.79, "word": " comparison", "probability": 0.73828125}, {"start": 982.79, "end": 983.31, "word": " test", "probability": 0.86669921875}, {"start": 983.31, "end": 983.83, "word": " ุทุจุนุง", "probability": 0.86767578125}, {"start": 983.83, "end": 984.11, "word": " ู
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", "probability": 0.93701171875}, {"start": 991.43, "end": 991.71, "word": " ุชููู", "probability": 0.963623046875}, {"start": 991.71, "end": 992.23, "word": " converge", "probability": 0.90380859375}, {"start": 992.23, "end": 992.55, "word": " ุทุจุนุง", "probability": 0.9571533203125}, {"start": 992.55, "end": 992.73, "word": " ูู", "probability": 0.7431640625}, {"start": 992.73, "end": 993.27, "word": " converge", "probability": 0.94091796875}, {"start": 993.27, "end": 993.63, "word": " ูุฅููุง", "probability": 0.7509765625}, {"start": 993.63, "end": 993.75, "word": " ูู", "probability": 0.389404296875}, {"start": 993.75, "end": 994.09, "word": " series", "probability": 0.63818359375}, {"start": 994.09, "end": 994.43, "word": " P2", "probability": 0.712158203125}, {"start": 994.43, "end": 994.57, "word": " ุณูุงุก", "probability": 0.4057159423828125}, {"start": 994.57, "end": 994.81, "word": " ุงุชููู", "probability": 0.82421875}, {"start": 994.81, "end": 995.13, "word": " ุงูุจุฑ", "probability": 0.8544921875}, {"start": 995.13, "end": 995.29, "word": " ู
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ูุงุฌููุง ุฏุง ูุฏุฑ ุทุจุนุง ุจูุนุฑู ุงู ูู ุงู N ุฃูู ุฃู ูุณุงูู N ุฃู ุงู C ู C ุฃูุจุฑ ู
ู ุงูุณูุฑ ุจููุณู
ุงูุทุฑููู ุนูู N ุชุฑุจูุน ุฒุงุฆุฏ ูุงุญุฏ ุงูุงู ุจุฏู ุงูุง ุงุชุฎูุต ููุง ู
ู ุงููุงุญุฏ ูู
ุง ุงุตุบุฑ ุงูู
ูุงู
ุจููุจุฑ ุงููุซู ุจููุจุฑ ุงููุซู ูุจุดูู ุงูู
ูุฌุฉ ุจูุงุญุฏ ุจุฎูู ุจุณ N ุชุฑุจูุน ูุจุชููู
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ุง ูู ุงููุจูุฑุฉ ุจุฏููุง ุชููู converge ุนุดุงู ุชููู converge ูุฃู 2 ูุงูุต C ุชููู ุฃูุจุฑ ู
ู 1 ููู ุงุฎุชุฑุช C ุชุณุงูู ูุต ูุนูู C .. ูุฏ C ุชุณุงูู ูุต ุจุชุตูุฑ ูุฐู N ุฃูุตุฑ 3 ุนูู 2 ุฃูุจุฑ ู
ู 1 converge ุฅุฐู ุจุชุตูุฑ ุนูุฏูุง ูู ุงู N ุนูู N ุชูุจู ุฒุงุฆุฏ 1 ุฃูู ู
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ู 1 ุฅุฐุง ุตุงุฑุช ููุฏู ุงู summation ุจุงู absolute value converge ูุจุงูุชุงูู ุงู series ุชุจุนุชู converge absolutely", "tokens": [6027, 7649, 2423, 28811, 5296, 4587, 7578, 502, 12, 18, 6225, 568, 41881, 5296, 33456, 11296, 430, 13934, 430, 6055, 3794, 995, 2407, 10632, 805, 6225, 568, 5551, 4117, 26890, 9154, 502, 11933, 15730, 20328, 9640, 2655, 8032, 1863, 16254, 2423, 28811, 20666, 8236, 2158, 41881, 46599, 6027, 2655, 6027, 1829, 2423, 2638, 6055, 3555, 3615, 31371, 41881, 3122], "avg_logprob": -0.38307291517655057, "compression_ratio": 1.4191616766467066, "no_speech_prob": 0.0, "words": [{"start": 1086.83, "end": 1087.17, "word": "ุงูุงู", "probability": 0.46612548828125}, {"start": 1087.17, "end": 1087.27, "word": " ุงู", "probability": 0.529296875}, {"start": 1087.27, "end": 1087.61, "word": " summation", "probability": 0.6044921875}, {"start": 1087.61, "end": 1087.97, "word": " ููู", "probability": 0.5834147135416666}, {"start": 1087.97, "end": 1088.33, "word": " 1", "probability": 0.7255859375}, {"start": 1088.33, "end": 1089.57, "word": "-3", "probability": 0.6605224609375}, {"start": 1089.57, "end": 1089.71, "word": " ุน", "probability": 0.01389312744140625}, {"start": 1089.71, "end": 1089.89, "word": " 2", "probability": 0.9111328125}, {"start": 1089.89, "end": 1090.31, "word": " converge", "probability": 0.339111328125}, {"start": 1090.31, "end": 1090.79, "word": " ูุฃููุง", "probability": 0.7423502604166666}, {"start": 1090.79, "end": 1090.97, "word": " P", "probability": 0.76904296875}, {"start": 1090.97, "end": 1091.35, "word": " Series", "probability": 0.5234375}, {"start": 1091.35, "end": 1091.85, "word": " P", "probability": 0.55029296875}, {"start": 1091.85, "end": 1092.27, "word": " ุชุณุงููุฉ", "probability": 0.68505859375}, {"start": 1092.27, "end": 1092.55, "word": " 3", "probability": 0.7685546875}, {"start": 1092.55, "end": 1092.75, "word": " ุน", "probability": 0.85400390625}, {"start": 1092.75, "end": 1092.93, "word": " 2", "probability": 0.95654296875}, {"start": 1092.93, "end": 1093.27, "word": " ุฃูุจุฑ", "probability": 0.8435872395833334}, {"start": 1093.27, "end": 1093.43, "word": " ู
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ู
ุด ูุงูุต ูุงุญุฏ ููุณ N ูู ุงู Inter P ุนูู Inter K ุฒุงุฆุฏ ูุงุญุฏ ููููุง ูู ูุฐู ุงูุฃุณุฆูุฉ ูุดูููุง converge absolute ุงู conventional", "tokens": [6027, 3794, 33604, 6027, 13672, 7578, 39182, 3224, 20328, 2304, 2304, 8592, 8717, 995, 4587, 9381, 36764, 24401, 12174, 41779, 426, 8978, 2423, 5751, 430, 15844, 5751, 591, 30767, 16373, 3215, 36764, 24401, 12174, 12610, 8315, 28242, 29538, 16247, 3794, 19986, 37977, 8717, 8592, 38688, 11296, 41881, 8236, 1975, 2407, 416, 46105], "avg_logprob": -0.4089032973883287, "compression_ratio": 1.3076923076923077, "no_speech_prob": 0.0, "words": [{"start": 1109.01, "end": 1109.41, "word": "ุงูุณุคุงู", "probability": 0.914306640625}, {"start": 1109.41, "end": 1109.53, "word": " ุงููู", "probability": 0.5927734375}, {"start": 1109.53, "end": 1109.81, "word": " ุจุนุฏู", "probability": 0.8388671875}, {"start": 1109.81, "end": 1110.23, "word": " ุตู
ู
ุด", "probability": 0.56512451171875}, {"start": 1110.23, "end": 1110.63, "word": " ูุงูุต", "probability": 0.744384765625}, {"start": 1110.63, "end": 1110.91, "word": " ูุงุญุฏ", "probability": 0.83203125}, {"start": 1110.91, "end": 1111.15, "word": " ููุณ", "probability": 0.5252685546875}, {"start": 1111.15, "end": 1111.45, "word": " N", "probability": 0.4658203125}, {"start": 1111.45, "end": 1111.85, "word": " ูู", "probability": 0.276611328125}, {"start": 1111.85, "end": 1111.95, "word": " ุงู", "probability": 0.6123046875}, {"start": 1111.95, "end": 1112.13, "word": " Inter", "probability": 0.178466796875}, {"start": 1112.13, "end": 1112.31, "word": " P", "probability": 0.51416015625}, {"start": 1112.31, "end": 1112.51, "word": " ุนูู", "probability": 0.681640625}, {"start": 1112.51, "end": 1112.73, "word": " Inter", "probability": 0.830078125}, {"start": 1112.73, "end": 1112.95, "word": " K", "probability": 0.88525390625}, {"start": 1112.95, "end": 1113.39, "word": " ุฒุงุฆุฏ", "probability": 0.73046875}, {"start": 1113.39, "end": 1114.07, "word": " ูุงุญุฏ", "probability": 0.973388671875}, {"start": 1114.07, "end": 1114.53, "word": " ููููุง", "probability": 0.7584635416666666}, {"start": 1114.53, "end": 1114.69, "word": " ูู", "probability": 0.900390625}, {"start": 1114.69, "end": 1114.87, "word": " ูุฐู", "probability": 0.892578125}, {"start": 1114.87, "end": 1115.35, "word": " ุงูุฃุณุฆูุฉ", "probability": 0.9688720703125}, {"start": 1115.35, "end": 1116.61, "word": " ูุดูููุง", "probability": 0.79443359375}, {"start": 1116.61, "end": 1116.91, "word": " converge", "probability": 0.720703125}, {"start": 1116.91, "end": 1117.31, "word": " absolute", "probability": 0.39453125}, {"start": 1117.31, "end": 1117.59, "word": " ุงู", "probability": 0.749267578125}, {"start": 1117.59, "end": 1117.99, "word": " conventional", "probability": 0.2685546875}], "temperature": 1.0}, {"id": 49, "seek": 114032, "start": 1118.64, "end": 1140.32, "text": "ุงูุฃู ูุดูู ุงูู Absolute Value ุงููู ูู summation ุจูุฑูุญ ู
ู ุฃูุตุฑ ูุงุญุฏ ููุตุฑ N ุจุธูุฑ ุงูู Inter V ุนูู Inter K ุจุฒุงูุฏ ูุงุญุฏ ุงูุงู ุจุฏูุง ูุนู
ู ุนูู ูุฐู ุงู test ุงู ุฎู
ุณ test ูุณุชุฎุฏู
ูุง ูุณุชุฎุฏู
ุทุจุนุง ููุง limit comparison test ูุนูู ุจุงุฎุฏ ุฃุนูู ุฃุณ ูู ุงู bus ุนูู ุฃุนูู ุฃุณ ูู ุงูู
ูุงู ูุจุทูุน ุนูุฏู ูุงุญุฏ ุนูู N ุงูุงู ุงู serious ุชุจุนุชู ุฃูู ุฅูุด ุทุจุนุง ุจุดูู ุงู limit ุฃู ูู
ุงูุชูุชูู ุฌุฑุคุฉ ุฏุณู
ุฑูุงุช", "tokens": [6027, 33456, 8717, 8592, 38688, 2423, 39184, 43965, 1169, 39352, 13672, 1829, 39896, 2408, 76, 399, 4724, 13546, 2407, 5016, 9154, 5551, 4587, 9381, 2288, 36764, 24401, 4032, 4587, 9381, 2288, 426, 4724, 19913, 3224, 2288, 2423, 39184, 5751, 691, 15844, 5751, 591, 4724, 11622, 995, 25708, 36764, 24401, 2423, 7649, 47525, 8315, 8717, 25957, 1211, 15844, 29538, 2423, 1500, 16472, 16490, 2304, 3794, 1500, 8717, 14851, 9778, 40448, 11296, 8717, 14851, 9778, 40448, 23032, 3555, 3615, 995, 34105, 4948, 9660, 1500, 37495, 22653, 4724, 47283, 3215, 5551, 3615, 23942, 5551, 3794, 8978, 2423, 1255, 15844, 5551, 3615, 23942, 5551, 3794, 8978, 9673, 41361, 6156, 3555, 9566, 1211, 3615, 43242, 3224, 36764, 24401, 15844, 426, 2423, 7649, 2423, 3156, 6055, 3555, 3615, 31371, 5551, 12610, 11933, 1829, 8592, 23032, 3555, 3615, 995, 4724, 8592, 38688, 2423, 4948, 14739, 8032, 2304, 16712, 29399, 9957, 10874, 2288, 33604, 3660, 11778, 38251, 16572, 9307], "avg_logprob": -0.35444077908208493, "compression_ratio": 1.7717041800643087, "no_speech_prob": 0.0, "words": [{"start": 1118.64, "end": 1118.98, "word": "ุงูุฃู", "probability": 0.5975341796875}, {"start": 1118.98, "end": 1119.3, "word": " ูุดูู", "probability": 0.8536783854166666}, {"start": 1119.3, "end": 1119.44, "word": " ุงูู", "probability": 0.689208984375}, {"start": 1119.44, "end": 1119.76, "word": " Absolute", "probability": 0.7269287109375}, {"start": 1119.76, "end": 1120.16, "word": " Value", "probability": 0.67236328125}, {"start": 1120.16, "end": 1120.64, "word": " ุงููู", "probability": 0.5032958984375}, {"start": 1120.64, "end": 1120.78, "word": " ูู", "probability": 0.65087890625}, {"start": 1120.78, "end": 1121.22, "word": " summation", "probability": 0.6331380208333334}, {"start": 1121.22, "end": 1121.52, "word": " ุจูุฑูุญ", "probability": 0.78326416015625}, {"start": 1121.52, "end": 1121.62, "word": " ู
ู", "probability": 0.231201171875}, {"start": 1121.62, "end": 1121.86, "word": " ุฃูุตุฑ", "probability": 0.6530914306640625}, {"start": 1121.86, "end": 1122.06, "word": " ูุงุญุฏ", "probability": 0.85205078125}, {"start": 1122.06, "end": 1122.32, "word": " ููุตุฑ", "probability": 0.541412353515625}, {"start": 1122.32, "end": 1122.4, "word": " N", "probability": 0.2222900390625}, {"start": 1122.4, "end": 1122.62, "word": " ุจุธูุฑ", "probability": 0.7596435546875}, {"start": 1122.62, "end": 1122.72, "word": " ุงูู", "probability": 0.533203125}, {"start": 1122.72, "end": 1122.84, "word": " Inter", "probability": 0.356201171875}, {"start": 1122.84, "end": 1123.04, "word": " V", "probability": 0.57421875}, {"start": 1123.04, "end": 1123.2, "word": " ุนูู", "probability": 0.66943359375}, {"start": 1123.2, "end": 1123.4, "word": " Inter", "probability": 0.68115234375}, {"start": 1123.4, "end": 1123.58, "word": " K", "probability": 0.76806640625}, {"start": 1123.58, "end": 1123.86, "word": " ุจุฒุงูุฏ", "probability": 0.742919921875}, {"start": 1123.86, "end": 1124.28, "word": " ูุงุญุฏ", "probability": 0.935546875}, {"start": 1124.28, "end": 1125.1, "word": " ุงูุงู", "probability": 0.564697265625}, {"start": 1125.1, "end": 1125.32, "word": " ุจุฏูุง", "probability": 0.62109375}, {"start": 1125.32, "end": 1125.54, "word": " ูุนู
ู", "probability": 0.9921875}, {"start": 1125.54, "end": 1125.68, "word": " ุนูู", "probability": 0.7939453125}, {"start": 1125.68, "end": 1125.88, "word": " ูุฐู", "probability": 0.767578125}, {"start": 1125.88, "end": 1126.3, "word": " ุงู", "probability": 0.837890625}, {"start": 1126.3, "end": 1126.3, "word": " test", "probability": 0.430419921875}, {"start": 1126.3, "end": 1126.56, "word": " ุงู", "probability": 0.3291015625}, {"start": 1126.56, "end": 1126.96, "word": " ุฎู
ุณ", "probability": 0.8780924479166666}, {"start": 1126.96, "end": 1127.18, "word": " test", "probability": 0.70361328125}, {"start": 1127.18, "end": 1128.02, "word": " ูุณุชุฎุฏู
ูุง", "probability": 0.91103515625}, {"start": 1128.02, "end": 1128.44, "word": " ูุณุชุฎุฏู
", "probability": 0.8642578125}, {"start": 1128.44, "end": 1128.72, "word": " ุทุจุนุง", "probability": 0.7969970703125}, {"start": 1128.72, "end": 1128.88, "word": " ููุง", "probability": 0.9208984375}, {"start": 1128.88, "end": 1129.18, "word": " limit", "probability": 0.5390625}, {"start": 1129.18, "end": 1129.66, "word": " comparison", "probability": 0.8837890625}, {"start": 1129.66, "end": 1130.04, "word": " test", "probability": 0.93603515625}, {"start": 1130.04, "end": 1130.76, "word": " ูุนูู", "probability": 0.916259765625}, {"start": 1130.76, "end": 1131.06, "word": " ุจุงุฎุฏ", "probability": 0.9557291666666666}, {"start": 1131.06, "end": 1131.3, "word": " ุฃุนูู", "probability": 0.94091796875}, {"start": 1131.3, "end": 1131.48, "word": " ุฃุณ", "probability": 0.807373046875}, {"start": 1131.48, "end": 1131.58, "word": " ูู", "probability": 0.64892578125}, {"start": 1131.58, "end": 1131.68, "word": " ุงู", "probability": 0.55078125}, {"start": 1131.68, "end": 1131.82, "word": " bus", "probability": 0.748046875}, {"start": 1131.82, "end": 1132.02, "word": " ุนูู", "probability": 0.6962890625}, {"start": 1132.02, "end": 1132.28, "word": " ุฃุนูู", "probability": 0.97900390625}, {"start": 1132.28, "end": 1132.48, "word": " ุฃุณ", "probability": 0.976806640625}, {"start": 1132.48, "end": 1132.6, "word": " ูู", "probability": 0.9560546875}, {"start": 1132.6, "end": 1133.0, "word": " ุงูู
ูุงู", "probability": 0.7470703125}, {"start": 1133.0, "end": 1133.74, "word": " ูุจุทูุน", "probability": 0.94306640625}, {"start": 1133.74, "end": 1134.0, "word": " ุนูุฏู", "probability": 0.6070556640625}, {"start": 1134.0, "end": 1134.28, "word": " ูุงุญุฏ", "probability": 0.7607421875}, {"start": 1134.28, "end": 1134.42, "word": " ุนูู", "probability": 0.85986328125}, {"start": 1134.42, "end": 1134.68, "word": " N", "probability": 0.79345703125}, {"start": 1134.68, "end": 1135.4, "word": " ุงูุงู", "probability": 0.781494140625}, {"start": 1135.4, "end": 1135.52, "word": " ุงู", "probability": 0.9619140625}, {"start": 1135.52, "end": 1135.72, "word": " serious", "probability": 0.833984375}, {"start": 1135.72, "end": 1136.22, "word": " ุชุจุนุชู", "probability": 0.771270751953125}, {"start": 1136.22, "end": 1136.68, "word": " ุฃูู", "probability": 0.85107421875}, {"start": 1136.68, "end": 1136.82, "word": " ุฅูุด", "probability": 0.6472981770833334}, {"start": 1136.82, "end": 1137.0, "word": " ุทุจุนุง", "probability": 0.8646240234375}, {"start": 1137.0, "end": 1137.28, "word": " ุจุดูู", "probability": 0.8055013020833334}, {"start": 1137.28, "end": 1137.4, "word": " ุงู", "probability": 0.767578125}, {"start": 1137.4, "end": 1137.62, "word": " limit", "probability": 0.9775390625}, {"start": 1137.62, "end": 1137.8, "word": " ุฃู", "probability": 0.365234375}, {"start": 1137.8, "end": 1137.92, "word": " ูู
", "probability": 0.5731201171875}, {"start": 1137.92, "end": 1138.52, "word": " ุงูุชูุชูู", "probability": 0.6698404947916666}, {"start": 1138.52, "end": 1139.7, "word": " ุฌุฑุคุฉ", "probability": 0.43060302734375}, {"start": 1139.7, "end": 1140.32, "word": " ุฏุณู
ุฑูุงุช", "probability": 0.73992919921875}], "temperature": 1.0}, {"id": 50, "seek": 116294, "start": 1140.82, "end": 1162.94, "text": "ูุงู limit ูุฐู ุนูู ูุฐู ุจุทูุน ุงู limit ูุงุญุฏ ูุจูู ุงู two two grow at the same rate ุงูุตู
ู
ุด ุงููู ูุงุญุฏ ุนูู n diverge ูุฅููุง harmonic series ูุจุงูุชุงูู ุงู series of positive terms ูุฐู ูู absolute value diverge ูุฐุง ูุง ูุคุฏู ุฅู ุงู series ุชุจุนุชู ุงูุฃุตููุฉ diverge ุฅุฐู we have to apply the three conditions ู
ุฏุงู
ูุฐู diverge ุจูุฑูุญ ูุญูู ุงูุชูุช ุดุฑูุท ูุดูู ูู
ู
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ู
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ุชุญููุฉ", "probability": 0.8709716796875}, {"start": 1162.52, "end": 1162.68, "word": " ููุง", "probability": 0.53076171875}, {"start": 1162.68, "end": 1162.94, "word": " ูุฃ", "probability": 0.90380859375}], "temperature": 1.0}, {"id": 51, "seek": 118669, "start": 1163.55, "end": 1186.69, "text": "ุงูู UN ุชุณุงูู N ุชุฑุจูุน ุนูู N ุชููุจ ุฒุงุฆุฏ ูุงุญุฏุ ุทุจุนุง ูู ู
ูุฌุจุฉุ ุงูู
ุดุชูุฉ ุชุจุนุชูุง ุงููู ูู N ูู ุงุชููู ูุงูุต N ุชููุจ ุนูู ูุฐุง ุงูููุงุญุ ุงูุงู ูู
ุง ุงู N ุนูุฏ ุงููุงุญุฏ ูู ุจุฏุจุฏูุง ู
ู ูุงุญุฏุ ุจุชุธููุง positive ูุนููุ ููู ูู N ุจุฏูุชูุง ู
ู ุงุชูููุ ุจูุตูุฑ ูุฐุง ุงููู ูุฐุง ุฅูุด ูุฐุง term negativeุ ูุจูู power N ุฃูุจุฑ ุฃู ูุณุงูู ุงูุฃุชูููุ ุจุชููู ูุฐู decreasing", "tokens": [6027, 39184, 8229, 6055, 3794, 995, 45865, 426, 6055, 2288, 21292, 3615, 15844, 426, 6055, 4117, 1829, 3555, 30767, 16373, 3215, 36764, 24401, 12399, 23032, 3555, 3615, 995, 39896, 3714, 29245, 49401, 12399, 9673, 8592, 2655, 28671, 6055, 3555, 34268, 11296, 13672, 1829, 39896, 426, 8978, 1975, 2655, 1863, 9957, 8717, 995, 4587, 9381, 426, 6055, 4117, 1829, 3555, 15844, 23758, 27188, 15040, 5016, 12399, 2423, 7649, 5296, 15042, 2423, 426, 43242, 2423, 14407, 24401, 45164, 47525, 44510, 11296, 9154, 36764, 24401, 12399, 39894, 19913, 1211, 11296, 3353, 37495, 22653, 12399, 44381, 45164, 426, 47525, 1211, 2655, 11296, 9154, 1975, 2655, 1863, 9957, 12399, 4724, 1829, 9381, 13546, 23758, 13672, 1829, 23758, 11933, 1829, 8592, 23758, 1433, 3671, 12399, 7251, 3555, 4587, 7578, 1347, 426, 5551, 4117, 26890, 34051, 7251, 3794, 995, 45865, 16247, 2655, 1863, 9957, 12399, 39894, 30544, 29538, 23223], "avg_logprob": -0.2593968460609863, "compression_ratio": 1.822695035460993, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1163.55, "end": 1164.09, "word": "ุงูู", "probability": 0.474609375}, {"start": 1164.09, "end": 1164.29, "word": " UN", "probability": 0.3759765625}, {"start": 1164.29, "end": 1164.79, "word": " ุชุณุงูู", "probability": 0.7569580078125}, {"start": 1164.79, "end": 1164.99, "word": " N", "probability": 0.64111328125}, {"start": 1164.99, "end": 1165.37, "word": " ุชุฑุจูุน", "probability": 0.7578125}, {"start": 1165.37, "end": 1165.51, "word": " ุนูู", "probability": 0.724609375}, {"start": 1165.51, "end": 1165.67, "word": " N", "probability": 0.92041015625}, {"start": 1165.67, "end": 1165.89, "word": " ุชููุจ", "probability": 0.5926513671875}, {"start": 1165.89, "end": 1166.15, "word": " ุฒุงุฆุฏ", "probability": 0.8922526041666666}, {"start": 1166.15, "end": 1166.65, "word": " ูุงุญุฏุ", "probability": 0.7762858072916666}, {"start": 1166.65, "end": 1166.93, "word": " ุทุจุนุง", "probability": 0.9278564453125}, {"start": 1166.93, "end": 1167.09, "word": " ูู", "probability": 0.7373046875}, {"start": 1167.09, "end": 1168.15, "word": " ู
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ู ุฅุชูููุ ู
ุงูู ู
ุดููุฉ ุงู series ุงูู
ุจููุฉ ู
ู ูุงุญุฏ ูููุง ุฃูุทุจู ุงูุดุฑุท ู
ู ุฅุชููู ุงู limit ู enter ุจูู ุนูู enter ูุฅุฒุงู ุงููุงุญุฏ ูุณุงูู ุณูุฑ ูุฃู ุฏุฑุฌุฉ ุงู bus ุฃูู ู
ู ุฏุฑุฌุฉ ุงูู
ูุงู
ูุจุงูุชุงูู ุชูุช ุดุฑูุท ุชุญููุงุช ุฅุฐู ุงู series ูู ูุฐู ุงูุญุงูุฉ ู
ููู
convert conditionally convert conditionally ุฅูุด ูุนูู convert conditionally ูุนูู ุจุงู absolute value diverse ููู ู
ุด ุชูุช ุดุฑูุท ุชุญููู conditions ูุนูู ุงูุดุฑูุท", "tokens": [28814, 8848, 1863, 34105, 47525, 10721, 8315, 11933, 3615, 8592, 3660, 34105, 9154, 11933, 2655, 1863, 9957, 12399, 19446, 41185, 37893, 28820, 3660, 2423, 2638, 9673, 3555, 1863, 10632, 9154, 36764, 24401, 37037, 8315, 14739, 9566, 3555, 4587, 25124, 2288, 9566, 9154, 11933, 2655, 1863, 9957, 2423, 4948, 5296, 3242, 4724, 1829, 3224, 15844, 3242, 9122, 28814, 11622, 995, 4587, 2423, 14407, 24401, 7251, 3794, 995, 45865, 8608, 5172, 2288, 5296, 33456, 11778, 47341, 3660, 2423, 1255, 5551, 4587, 1211, 9154, 11778, 47341, 3660, 9673, 4587, 10943, 46599, 6027, 2655, 6027, 1829, 6055, 1211, 2655, 13412, 32887, 9566, 6055, 5016, 4587, 4587, 9307, 11933, 8848, 1863, 2423, 2638, 8978, 29538, 21542, 6027, 3660, 3714, 4587, 2407, 2304, 7620, 4188, 379, 7620, 4188, 379, 11933, 1829, 8592, 37495, 22653, 7620, 4188, 379, 37495, 22653, 20666, 8236, 2158, 9521, 44381, 37893, 6055, 1211, 2655, 13412, 32887, 9566, 6055, 5016, 4587, 4587, 4117, 4487, 37495, 22653, 25124, 32887, 9566], "avg_logprob": -0.3256369510274025, "compression_ratio": 2.0305084745762714, "no_speech_prob": 3.5762786865234375e-07, "words": [{"start": 1187.83, "end": 1188.17, "word": "ุฅุฐู", "probability": 0.430419921875}, {"start": 1188.17, "end": 1188.33, "word": " ููุง", "probability": 0.646484375}, {"start": 1188.33, "end": 1188.65, "word": " ุจุฏุฃูุง", "probability": 0.7608235677083334}, {"start": 1188.65, "end": 1188.87, "word": " ุฅุนุดุฉ", "probability": 0.5986328125}, {"start": 1188.87, "end": 1189.05, "word": " ููุง", "probability": 0.453369140625}, {"start": 1189.05, "end": 1189.17, "word": " ู
ู", "probability": 0.9775390625}, {"start": 1189.17, "end": 1189.51, "word": " ุฅุชูููุ", "probability": 0.687890625}, {"start": 1189.51, "end": 1189.57, "word": " ู
ุงูู", "probability": 0.580078125}, {"start": 1189.57, "end": 1190.11, "word": " ู
ุดููุฉ", "probability": 0.9842122395833334}, {"start": 1190.11, "end": 1190.43, "word": " ุงู", "probability": 0.42822265625}, {"start": 1190.43, "end": 1190.61, "word": " series", "probability": 0.1881103515625}, {"start": 1190.61, "end": 1190.97, "word": " ุงูู
ุจููุฉ", "probability": 0.702880859375}, {"start": 1190.97, "end": 1191.11, "word": " ู
ู", "probability": 0.97998046875}, {"start": 1191.11, "end": 1191.41, "word": " ูุงุญุฏ", "probability": 0.96875}, {"start": 1191.41, "end": 1191.69, "word": " ูููุง", "probability": 0.789794921875}, {"start": 1191.69, "end": 1192.07, "word": " ุฃูุทุจู", "probability": 0.823974609375}, {"start": 1192.07, "end": 1192.43, "word": " ุงูุดุฑุท", "probability": 0.9573567708333334}, {"start": 1192.43, "end": 1192.61, "word": " ู
ู", "probability": 0.9658203125}, {"start": 1192.61, "end": 1193.47, "word": " ุฅุชููู", "probability": 0.86474609375}, {"start": 1193.47, "end": 1193.89, "word": " ุงู", "probability": 0.6298828125}, {"start": 1193.89, "end": 1194.21, "word": " limit", "probability": 0.94677734375}, {"start": 1194.21, "end": 1194.47, "word": " ู", "probability": 0.83056640625}, {"start": 1194.47, "end": 1194.75, "word": " enter", "probability": 0.11614990234375}, {"start": 1194.75, "end": 1194.93, "word": " ุจูู", "probability": 0.6546223958333334}, {"start": 1194.93, "end": 1195.05, "word": " ุนูู", "probability": 0.79443359375}, {"start": 1195.05, "end": 1195.27, "word": " enter", "probability": 0.6435546875}, {"start": 1195.27, "end": 1195.57, "word": " ูุฅุฒุงู", "probability": 0.690673828125}, {"start": 1195.57, "end": 1195.83, "word": " ุงููุงุญุฏ", "probability": 0.7432454427083334}, {"start": 1195.83, "end": 1196.13, "word": " ูุณุงูู", "probability": 0.9149169921875}, {"start": 1196.13, "end": 1196.45, "word": " ุณูุฑ", "probability": 0.7162272135416666}, {"start": 1196.45, "end": 1196.67, "word": " ูุฃู", "probability": 0.723388671875}, {"start": 1196.67, "end": 1197.07, "word": " ุฏุฑุฌุฉ", "probability": 0.96240234375}, {"start": 1197.07, "end": 1197.17, "word": " ุงู", "probability": 0.40966796875}, {"start": 1197.17, "end": 1197.29, "word": " bus", "probability": 0.5341796875}, {"start": 1197.29, "end": 1197.61, "word": " ุฃูู", "probability": 0.9500325520833334}, {"start": 1197.61, "end": 1197.73, "word": " ู
ู", "probability": 0.9853515625}, {"start": 1197.73, "end": 1198.09, "word": " ุฏุฑุฌุฉ", "probability": 0.990234375}, {"start": 1198.09, "end": 1198.77, "word": " ุงูู
ูุงู
", "probability": 0.88232421875}, {"start": 1198.77, "end": 1199.45, "word": " ูุจุงูุชุงูู", "probability": 0.90810546875}, {"start": 1199.45, "end": 1199.73, "word": " ุชูุช", "probability": 0.74951171875}, {"start": 1199.73, "end": 1199.97, "word": " ุดุฑูุท", "probability": 0.9251302083333334}, {"start": 1199.97, "end": 1200.55, "word": " ุชุญููุงุช", "probability": 0.742919921875}, {"start": 1200.55, "end": 1200.85, "word": " ุฅุฐู", "probability": 0.6289876302083334}, {"start": 1200.85, "end": 1200.95, "word": " ุงู", "probability": 0.96875}, {"start": 1200.95, "end": 1201.15, "word": " series", "probability": 0.91357421875}, {"start": 1201.15, "end": 1201.31, "word": " ูู", "probability": 0.86865234375}, {"start": 1201.31, "end": 1201.45, "word": " ูุฐู", "probability": 0.7216796875}, {"start": 1201.45, "end": 1201.71, "word": " ุงูุญุงูุฉ", "probability": 0.98046875}, {"start": 1201.71, "end": 1201.87, "word": " ู
ููู
", "probability": 0.31854248046875}, {"start": 1201.87, "end": 1202.37, "word": " convert", "probability": 0.07073974609375}, {"start": 1202.37, "end": 1203.21, "word": " conditionally", "probability": 0.84033203125}, {"start": 1203.21, "end": 1203.83, "word": " convert", "probability": 0.449462890625}, {"start": 1203.83, "end": 1204.59, "word": " conditionally", "probability": 0.929931640625}, {"start": 1204.59, "end": 1204.79, "word": " ุฅูุด", "probability": 0.7862141927083334}, {"start": 1204.79, "end": 1204.95, "word": " ูุนูู", "probability": 0.973876953125}, {"start": 1204.95, "end": 1205.33, "word": " convert", "probability": 0.94580078125}, {"start": 1205.33, "end": 1205.93, "word": " conditionally", "probability": 0.94677734375}, {"start": 1205.93, "end": 1206.47, "word": " ูุนูู", "probability": 0.7403564453125}, {"start": 1206.47, "end": 1206.61, "word": " ุจุงู", "probability": 0.97900390625}, {"start": 1206.61, "end": 1206.91, "word": " absolute", "probability": 0.8525390625}, {"start": 1206.91, "end": 1207.25, "word": " value", "probability": 0.98193359375}, {"start": 1207.25, "end": 1207.73, "word": " diverse", "probability": 0.50732421875}, {"start": 1207.73, "end": 1208.23, "word": " ููู", "probability": 0.84033203125}, {"start": 1208.23, "end": 1208.45, "word": " ู
ุด", "probability": 0.78466796875}, {"start": 1208.45, "end": 1208.71, "word": " ุชูุช", "probability": 0.9645182291666666}, {"start": 1208.71, "end": 1209.11, "word": " ุดุฑูุท", "probability": 0.9816080729166666}, {"start": 1209.11, "end": 1209.87, "word": " ุชุญููู", "probability": 0.7943359375}, {"start": 1209.87, "end": 1211.13, "word": " conditions", "probability": 0.58984375}, {"start": 1211.13, "end": 1211.53, "word": " ูุนูู", "probability": 0.96142578125}, {"start": 1211.53, "end": 1211.97, "word": " ุงูุดุฑูุท", "probability": 0.958984375}], "temperature": 1.0}, {"id": 53, "seek": 123597, "start": 1213.41, "end": 1235.97, "text": "ุทูุจ ุงูุณุคุงู ุงููู ุจุนุฏ ุงูุตู
ุงุดู ูุงูุต 1 ุฃุณ N N ุซูุงุซุฉ ุฃุณ N ุนูู ุฃุฑุจุนุฉ ุฃุณ N ุงูุขู ุงูุตู
ุงุดู ูู absolute value ูู A N ุงููู ูู ุจุชุฑูุญ ูุงูุต ูุงุญุฏ ุฃุณ N ุจุถุงู ุงูุจุงูู ุงูุงู ูุฐุง ุจุฏูุง ูุนู
ูู test ุงููู ุจุฏูุง ูุนู
ูู ุงู road test ุงูุงู ุงูุฌุบู ุงููููู ูู absolute value ูู A N ุงููู ูู N ุฃุณ ูุงุญุฏ ุนูู N ูุซูุงุซุฉ ูุงูุงุฑุจุนุฉ ุจุฑูู ุงูุฃุณ N ุชุจุนูุง", "tokens": [9566, 1829, 3555, 21136, 33604, 6027, 13672, 7578, 39182, 31767, 2304, 33599, 1863, 8717, 995, 4587, 9381, 502, 5551, 3794, 426, 426, 38637, 1211, 5718, 104, 3660, 5551, 3794, 426, 15844, 5551, 25513, 27884, 5551, 3794, 426, 6024, 48506, 31767, 2304, 33599, 1863, 24976, 8236, 2158, 24976, 316, 426, 13672, 7578, 8032, 7578, 39894, 32887, 5016, 8717, 995, 4587, 9381, 36764, 24401, 5551, 3794, 426, 4724, 11242, 6027, 29739, 995, 4587, 7578, 2423, 7649, 23758, 47525, 8315, 8717, 25957, 43761, 1500, 13672, 7578, 47525, 8315, 8717, 25957, 43761, 2423, 3060, 1500, 2423, 7649, 25724, 17082, 1863, 28239, 11536, 7578, 24976, 8236, 2158, 24976, 316, 426, 13672, 7578, 8032, 7578, 426, 5551, 3794, 36764, 24401, 15844, 426, 4032, 12984, 1211, 5718, 104, 3660, 16070, 9640, 3555, 27884, 4724, 32887, 5172, 16247, 3794, 426, 6055, 3555, 3615, 11296], "avg_logprob": -0.2698448852901041, "compression_ratio": 2.1271929824561404, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1213.41, "end": 1213.71, "word": "ุทูุจ", "probability": 0.6638590494791666}, {"start": 1213.71, "end": 1213.97, "word": " ุงูุณุคุงู", "probability": 0.89501953125}, {"start": 1213.97, "end": 1214.09, "word": " ุงููู", "probability": 0.770263671875}, {"start": 1214.09, "end": 1214.29, "word": " ุจุนุฏ", "probability": 0.9228515625}, {"start": 1214.29, "end": 1214.81, "word": " ุงูุตู
ุงุดู", "probability": 0.69732666015625}, {"start": 1214.81, "end": 1215.09, "word": " ูุงูุต", "probability": 0.702484130859375}, {"start": 1215.09, "end": 1215.29, "word": " 1", "probability": 0.58203125}, {"start": 1215.29, "end": 1215.49, "word": " ุฃุณ", "probability": 0.5635986328125}, {"start": 1215.49, "end": 1215.63, "word": " N", "probability": 0.50341796875}, {"start": 1215.63, "end": 1215.97, "word": " N", "probability": 0.46435546875}, {"start": 1215.97, "end": 1216.59, "word": " ุซูุงุซุฉ", "probability": 0.820068359375}, {"start": 1216.59, "end": 1216.77, "word": " ุฃุณ", "probability": 0.935791015625}, {"start": 1216.77, "end": 1216.97, "word": " N", "probability": 0.89111328125}, {"start": 1216.97, "end": 1217.17, "word": " ุนูู", "probability": 0.6025390625}, {"start": 1217.17, "end": 1217.55, "word": " ุฃุฑุจุนุฉ", "probability": 0.8211263020833334}, {"start": 1217.55, "end": 1217.81, "word": " ุฃุณ", "probability": 0.985595703125}, {"start": 1217.81, "end": 1218.05, "word": " N", "probability": 0.97119140625}, {"start": 1218.05, "end": 1218.83, "word": " ุงูุขู", "probability": 0.7037353515625}, {"start": 1218.83, "end": 1219.41, "word": " ุงูุตู
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ูู", "probability": 0.8458658854166666}, {"start": 1224.87, "end": 1225.39, "word": " test", "probability": 0.75439453125}, {"start": 1225.39, "end": 1226.11, "word": " ุงููู", "probability": 0.669677734375}, {"start": 1226.11, "end": 1226.33, "word": " ุจุฏูุง", "probability": 0.859375}, {"start": 1226.33, "end": 1226.65, "word": " ูุนู
ูู", "probability": 0.9690755208333334}, {"start": 1226.65, "end": 1226.79, "word": " ุงู", "probability": 0.58740234375}, {"start": 1226.79, "end": 1227.65, "word": " road", "probability": 0.54833984375}, {"start": 1227.65, "end": 1229.53, "word": " test", "probability": 0.9208984375}, {"start": 1229.53, "end": 1229.95, "word": " ุงูุงู", "probability": 0.784423828125}, {"start": 1229.95, "end": 1230.33, "word": " ุงูุฌุบู", "probability": 0.610107421875}, {"start": 1230.33, "end": 1230.67, "word": " ุงููููู", "probability": 0.7293294270833334}, {"start": 1230.67, "end": 1230.85, "word": " ูู", "probability": 0.92041015625}, {"start": 1230.85, "end": 1231.19, "word": " absolute", "probability": 0.96337890625}, {"start": 1231.19, "end": 1231.51, "word": " value", "probability": 0.99169921875}, {"start": 1231.51, "end": 1231.69, "word": " ูู", "probability": 0.95263671875}, {"start": 1231.69, "end": 1231.83, "word": " A", "probability": 0.96826171875}, {"start": 1231.83, "end": 1232.05, "word": " N", "probability": 0.9853515625}, {"start": 1232.05, "end": 1232.59, "word": " ุงููู", "probability": 0.9794921875}, {"start": 1232.59, "end": 1232.75, "word": " ูู", "probability": 0.95947265625}, {"start": 1232.75, "end": 1232.93, "word": " N", "probability": 0.9228515625}, {"start": 1232.93, "end": 1233.11, "word": " ุฃุณ", "probability": 0.95556640625}, {"start": 1233.11, "end": 1233.33, "word": " ูุงุญุฏ", "probability": 0.869873046875}, {"start": 1233.33, "end": 1233.47, "word": " ุนูู", "probability": 0.81689453125}, {"start": 1233.47, "end": 1233.71, "word": " N", "probability": 0.97021484375}, {"start": 1233.71, "end": 1234.31, "word": " ูุซูุงุซุฉ", "probability": 0.8142496744791666}, {"start": 1234.31, "end": 1234.69, "word": " ูุงูุงุฑุจุนุฉ", "probability": 0.768310546875}, {"start": 1234.69, "end": 1235.01, "word": " ุจุฑูู", "probability": 0.7518717447916666}, {"start": 1235.01, "end": 1235.31, "word": " ุงูุฃุณ", "probability": 0.825439453125}, {"start": 1235.31, "end": 1235.49, "word": " N", "probability": 0.9716796875}, {"start": 1235.49, "end": 1235.97, "word": " ุชุจุนูุง", "probability": 0.859375}], "temperature": 1.0}, {"id": 54, "seek": 125903, "start": 1236.41, "end": 1259.03, "text": "ุงูู Unlimited ู N ุฃุณ 1 ุนูู N ุจุงู Table ูุณูู 1 ูุจุถู ุนูุฏู 3 ุนูู 4 ุงูู 3 ุนูู 4 ุฃูู ู
ู 1 ูุจุงูุชุงูู ุงู series ุชุจุนุชู converge ุจุงู root 9 ุจุงู root 9 ุฅุฐุง ู
ูู ุงููู converge ููู ุงู absolute value ูุจุงูุชุงูู ุงู series ุชุจุนุชู ุจูููู ุนููุง converge absolutely ุนููุง absolutely ู
ุดููุฉ ูุฐู ู
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ูุดุฉ ูุงูุต 5 ุฃูุณ N ุนูู N ุฒุงุฆุฏ 5 ุฃูุณ N ุทุจุนุง ููุง ูุฐู ูุงูุต 5 ุฃูุณ N ูู ูุงูุต 1 ุฃูุณ N ูู 5 ุฃูุณ N ูู
ุง ุจุฏุฃ ุฃุฌูุจ ุงู absolute value ุจุชุดูู ูุงูุต 1 ุฃูุณ N ุจูุจูู 5 ุฃูุณ N ุนูู N ุฒุงุฆุฏ 5 ุฃูุณ N ุงูุขู ุจุฏูุง ูุดูู ุฅูุด .. ูุนู
ู ูุฐู ุงููู ูู ุงู .. ูุดูู ูู converge ููุง diverge", "tokens": [9566, 1829, 3555, 20328, 2304, 1829, 8592, 3660, 8717, 995, 4587, 9381, 1025, 5551, 10859, 3794, 426, 15844, 426, 30767, 16373, 3215, 1025, 5551, 10859, 3794, 426, 23032, 3555, 3615, 995, 34105, 29538, 8717, 995, 4587, 9381, 1025, 5551, 10859, 3794, 426, 39896, 8717, 995, 4587, 9381, 502, 5551, 10859, 3794, 426, 8978, 1025, 5551, 10859, 3794, 426, 5296, 15042, 47525, 10721, 5551, 7435, 1829, 3555, 2423, 8236, 2158, 39894, 8592, 26895, 8717, 995, 4587, 9381, 502, 5551, 10859, 3794, 426, 4724, 1829, 3555, 4587, 7578, 1025, 5551, 10859, 3794, 426, 15844, 426, 30767, 16373, 3215, 1025, 5551, 10859, 3794, 426, 6024, 48506, 47525, 8315, 8717, 8592, 38688, 11933, 1829, 8592, 4386, 8717, 25957, 1211, 29538, 13672, 1829, 31439, 2423, 4386, 8717, 8592, 38688, 8032, 7578, 41881, 49429, 18558, 432], "avg_logprob": -0.2393845383447545, "compression_ratio": 1.8564593301435406, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1261.35, "end": 1261.73, "word": "ุทูุจ", "probability": 0.6292724609375}, {"start": 1261.73, "end": 1262.25, "word": " ุตู
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ู ุงูุงูู ุงูู ุฏุฑุฌุฉ ุงู bus ุชุณุงูู ุฏุฑุฌุฉ ุงูู
ูุงู
ูุงู ุฎู
ุณุฉ ุฃุซููู ุงูุชุฑ ุงูุจุฑ ู
ู ุงู N ูุจุงูุชุงูู ุงุนูู ุฏุฑุฌุฉ ุงู bus ุฎู
ุณุฉ ุฃุซููู ู ุงุนูู ุฏุฑุฌุฉ ุงูู
ูุงู
ุฎู
ุณุฉ ุฃุซููู ุฒู ุจุนุถ ููุงุญุธุช ุงูู ูู ุนู
ูุช ุงู limit ุฅููุง ุจุทูุน ูุง ูุณุงูู ุณูุฑ ู limit ุฎู
ุณุฉ ุฃุซููู ุนูู N ุฒุงุฆุฏ ุฎู
ุณุฉ ุฃุซููู ูุณู
ูุง ุนูู ุฎู
ุณุฉ ุฃุซููู ุงู bus ู ุงูู
ูุงู
ุทูุน ูุงุญุฏ ู ููุง N ุนูู ุฎู
ุณุฉ ุฃุซููู ุฒุงุฆุฏ ูุงุญุฏ ูุงู N ุนูู ุฎู
ุณุฉ ุฃุซููู ูู ุนู
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ู ุจุฏูุง ูุฑูุญ ูุนู
ู ุจ three conditions ู three conditions ูุงุฎุฏ ุงู UN ูู ุงู UN ุชุจุนุชู ุงู UN ุทุจุนุง ู
ูุฌุจุฉ UN prime ุชุณุงูู ูุฐุง ุงูููุงู
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ุดุชูุฉ ุงูู
ุดุชูุฉ ู
ุด ูููุง ุฅุดุงุฑุฉ ุณุงูู
ุฉ ุจุงูู
ุฑุฉ ู ูู ุงู terms ู
ูุฌุจุฉ ูุจุงูุชุงูู ุงูู
ุดุชูุฉ ุชุจุนุชู ู
ูุฌุจุฉ ูุนูู ุงู UN increasing ุฅุฐุง ุงูุดุฑุท ุงูุชุงูู ููุท increasing ูุจุงูุชุงูู ูุฐุง ุงู test ุฅูุงุด fail ูุจูู ุจุฏูุง ูุฑูุญ ุฅูุงุด ูุนู
ู test ุขุฎุฑ ุงููู ูู ุงู intern test", "tokens": [3224, 1829, 9673, 8592, 2655, 28671, 9673, 8592, 2655, 28671, 37893, 8978, 11296, 11933, 8592, 9640, 3660, 8608, 45340, 3660, 20666, 2304, 25720, 4032, 28242, 2423, 2115, 3714, 29245, 49401, 46599, 6027, 2655, 6027, 1829, 9673, 8592, 2655, 28671, 6055, 3555, 3615, 31371, 3714, 29245, 49401, 37495, 22653, 2423, 8229, 5662, 11933, 15730, 25124, 2288, 9566, 16712, 7649, 1829, 6156, 47432, 5662, 46599, 6027, 2655, 6027, 1829, 23758, 2423, 1500, 11933, 1829, 33599, 3061, 7251, 3555, 4587, 7578, 47525, 8315, 8717, 32887, 5016, 11933, 1829, 33599, 8717, 25957, 1211, 1500, 19753, 34740, 13672, 1829, 31439, 2423, 2154, 1500], "avg_logprob": -0.21401515271928576, "compression_ratio": 1.8719211822660098, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1333.78, "end": 1334.32, "word": "ูู", "probability": 0.34344482421875}, {"start": 1334.32, "end": 1334.86, "word": " ุงูู
ุดุชูุฉ", "probability": 0.8575439453125}, {"start": 1334.86, "end": 1335.42, "word": " ุงูู
ุดุชูุฉ", "probability": 0.7926025390625}, {"start": 1335.42, "end": 1335.58, "word": " ู
ุด", "probability": 0.493896484375}, {"start": 1335.58, "end": 1335.8, "word": " ูููุง", "probability": 0.9013671875}, {"start": 1335.8, "end": 1336.14, "word": " ุฅุดุงุฑุฉ", "probability": 0.893310546875}, {"start": 1336.14, "end": 1336.46, "word": " ุณุงูู
ุฉ", "probability": 0.4950358072916667}, {"start": 1336.46, "end": 1336.78, "word": " ุจุงูู
ุฑุฉ", "probability": 0.88623046875}, {"start": 1336.78, "end": 1336.9, "word": " ู", "probability": 0.76416015625}, {"start": 1336.9, "end": 1337.06, "word": " ูู", "probability": 0.55078125}, {"start": 1337.06, "end": 1337.22, "word": " ุงู", "probability": 0.83642578125}, {"start": 1337.22, "end": 1337.5, "word": " terms", "probability": 0.568359375}, {"start": 1337.5, "end": 1338.08, "word": " ู
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ูุฌุจุฉ", "probability": 0.9718424479166666}, {"start": 1340.1, "end": 1340.62, "word": " ูุนูู", "probability": 0.946533203125}, {"start": 1340.62, "end": 1340.78, "word": " ุงู", "probability": 0.95263671875}, {"start": 1340.78, "end": 1341.0, "word": " UN", "probability": 0.66357421875}, {"start": 1341.0, "end": 1341.82, "word": " increasing", "probability": 0.9541015625}, {"start": 1341.82, "end": 1342.2, "word": " ุฅุฐุง", "probability": 0.762451171875}, {"start": 1342.2, "end": 1342.66, "word": " ุงูุดุฑุท", "probability": 0.8645833333333334}, {"start": 1342.66, "end": 1343.12, "word": " ุงูุชุงูู", "probability": 0.9168294270833334}, {"start": 1343.12, "end": 1343.44, "word": " ููุท", "probability": 0.8623046875}, {"start": 1343.44, "end": 1344.06, "word": " increasing", "probability": 0.95751953125}, {"start": 1344.06, "end": 1344.74, "word": " ูุจุงูุชุงูู", "probability": 0.9419921875}, {"start": 1344.74, "end": 1344.94, "word": " ูุฐุง", "probability": 0.90185546875}, {"start": 1344.94, "end": 1345.18, "word": " ุงู", "probability": 0.60595703125}, {"start": 1345.18, "end": 1345.18, "word": " test", "probability": 0.95751953125}, {"start": 1345.18, "end": 1345.5, "word": " ุฅูุงุด", "probability": 0.5423990885416666}, {"start": 1345.5, "end": 1346.22, "word": " fail", "probability": 0.6240234375}, {"start": 1346.22, "end": 1347.04, "word": " ูุจูู", "probability": 0.953125}, {"start": 1347.04, "end": 1347.4, "word": " ุจุฏูุง", "probability": 0.9033203125}, {"start": 1347.4, "end": 1347.58, "word": " ูุฑูุญ", "probability": 0.96826171875}, {"start": 1347.58, "end": 1347.82, "word": " ุฅูุงุด", "probability": 0.9508463541666666}, {"start": 1347.82, "end": 1348.48, "word": " ูุนู
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ูุฌุจ ุฃู ุณุงูู
1 ูุง ูุณุงูู 0 ูุจุงูุชุงูู ุงู series ุชุจุนุชู diverge ุงู series ุฅูุด diverge ุทุจุนุง ุฃูุง ุนู
ูุช ูู ูุฐุง ููู ุฅูุด ุจููุงุญููุด ููู ุฃูุช ู
ู ุงูุฃูู ู
ู ููุง ูู ูุงุญุธุช ู
ู ุงูุจุฏุงูุฉ ู
ู ููุง ุชุนู
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ู ููุง ูู
ุง ุนู
ููุง ุงู limit ุงุทูุน ูุงุญุฏ ู ุจุณ ุงููู ุจููุฑู ูุงูุต ูุงุญุฏ ูุต ุงู ู ูุงูุต ูุงุญุฏ ูุต ุงู limit ูู
ูุฌุจ ุงู ุณุงูุจ ูุงุญุฏ ูุจุงูุชุงูู ุจุชุธููุง ูุง ูุณุงูู ุณูุฑ ุงุฐุง ู
ู ุงูุฃูู ู
ู ุงูุจุฏุงูุฉ ู ูู ุนู
ููุง ุงู intern test ู ุทูุน ุงููุง ูุง ูุณุงูู ุณูุฑ ู ุงุณุชููุธ ููุด ุฏุงุนู ูุนู
ู ูู ูุฐุง ูู ูุฐุง ู
ุด ุฏุงุนู ุงูุด ุงู ุงุญูุง ููุฌุฃ ุงููู ููุฌุฃ ุงููู ููู ุงูุง ุงุนู
ูุช ููู ุนูุดุงู ุงูุชูุง ุชุดูููุง ุงูุฎุทูุงุช ุงููู ุจูู
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ู
ูู ุงูุฎุทูุฉ ุงูุฃุฎูุฑุฉ ู
ู ุงูุจุฏุงูุฉ ุฃููุง ูุนู
ููุง ุทูุจ ุงู summation ูุงูุต ูุงุญุฏ ุฃุณุฆู N factorial ูู ุชุฑุจูุน ุนูู ุชูุงุชุฉ N factorial ุงู series ููquotient term ูู ุนุจุงุฑุฉ ุนู ูุงูุต ูุงุญุฏ ุฃุณุฆู ุจูุทูุฑูุง ูุถู N factorial ุชุฑุจูุน ุนูู ุชูุงุชุฉ N factorial ุทุจุนุง ูุฌูุฏ ุงู factorial ุจูุญุชู
ุนูู ุฃูู ูุงุฒู
ุงุณุชุฎุฏู
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ูููุจุฉุ ุถุฑุจ ู
ูููุจุฉ ุงูุงุจ ุจุฏูุง ููู ูุฐู ูู
ุง ููุตููุง ูู N ูุจุชุตูุฑ N ุฒุงุฆุฏ ูุงุญุฏ ุชุฑุจูุน ู ููู ูุฐู ูู
ุง ููุตููุง ูุชูุงุชุฉ N ูุจููููุง ุชูุงุชุฉ N ุฒุงุฆุฏ ุชูุงุชุฉ ูู ุชูุงุชุฉ N ุฒุงุฆุฏ ุงุชููู ูู ุชูุงุชุฉ N ุฒุงุฆุฏ ูุงุญุฏ", "tokens": [5172, 3555, 1863, 7435, 1829, 3555, 624, 426, 30767, 16373, 3215, 36764, 24401, 15844, 624, 426, 7251, 3794, 995, 45865, 44945, 32887, 5016, 20666, 624, 426, 30767, 16373, 3215, 36764, 24401, 44945, 5016, 9566, 47525, 1211, 2423, 426, 426, 30767, 16373, 3215, 36764, 24401, 4032, 34105, 426, 30767, 16373, 3215, 36764, 24401, 39894, 9381, 13546, 37495, 22653, 6055, 1211, 9307, 3660, 426, 30767, 16373, 3215, 6055, 1211, 9307, 3660, 15844, 2423, 316, 426, 34051, 2423, 624, 426, 13672, 1829, 39896, 3714, 4587, 1211, 37746, 3660, 12399, 48812, 25513, 3714, 4587, 1211, 37746, 3660, 2423, 16758, 47525, 8315, 8717, 5172, 4117, 29538, 5296, 15042, 8717, 2407, 36520, 11296, 24976, 426, 6156, 3555, 2655, 9381, 13546, 426, 30767, 16373, 3215, 36764, 24401, 6055, 2288, 21292, 3615, 4032, 8717, 5172, 4117, 29538, 5296, 15042, 8717, 2407, 36520, 11296, 5296, 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ูููุจุฉุ", "probability": 0.7357584635416666}, {"start": 1439.08, "end": 1439.28, "word": " ุถุฑุจ", "probability": 0.9208984375}, {"start": 1439.28, "end": 1439.96, "word": " ู
ูููุจุฉ", "probability": 0.95380859375}, {"start": 1439.96, "end": 1440.7, "word": " ุงูุงุจ", "probability": 0.381103515625}, {"start": 1440.7, "end": 1440.9, "word": " ุจุฏูุง", "probability": 0.857421875}, {"start": 1440.9, "end": 1441.14, "word": " ููู", "probability": 0.9736328125}, {"start": 1441.14, "end": 1441.38, "word": " ูุฐู", "probability": 0.5224609375}, {"start": 1441.38, "end": 1441.58, "word": " ูู
ุง", "probability": 0.94091796875}, {"start": 1441.58, "end": 1442.04, "word": " ููุตููุง", "probability": 0.957763671875}, {"start": 1442.04, "end": 1442.2, "word": " ูู", "probability": 0.61181640625}, {"start": 1442.2, "end": 1442.4, "word": " N", "probability": 0.96728515625}, {"start": 1442.4, "end": 1442.86, "word": " ูุจุชุตูุฑ", "probability": 0.94619140625}, {"start": 1442.86, "end": 1443.0, "word": " N", "probability": 0.94384765625}, {"start": 1443.0, "end": 1443.26, "word": " ุฒุงุฆุฏ", "probability": 0.9674479166666666}, {"start": 1443.26, "end": 1443.5, "word": " ูุงุญุฏ", "probability": 0.984375}, {"start": 1443.5, "end": 1444.04, "word": " ุชุฑุจูุน", "probability": 0.9102783203125}, {"start": 1444.04, "end": 1444.44, "word": " ู", "probability": 0.9501953125}, {"start": 1444.44, "end": 1444.74, "word": " ููู", "probability": 0.8341471354166666}, {"start": 1444.74, "end": 1444.98, "word": " ูุฐู", "probability": 0.94482421875}, {"start": 1444.98, "end": 1445.2, "word": " ูู
ุง", "probability": 0.983642578125}, {"start": 1445.2, "end": 1445.64, "word": " ููุตููุง", "probability": 0.97998046875}, {"start": 1445.64, "end": 1446.14, "word": " ูุชูุงุชุฉ", "probability": 0.9490234375}, {"start": 1446.14, "end": 1446.28, "word": " N", "probability": 0.982421875}, {"start": 1446.28, "end": 1446.86, "word": " ูุจููููุง", "probability": 0.9619954427083334}, {"start": 1446.86, "end": 1447.2, "word": " ุชูุงุชุฉ", "probability": 0.9849853515625}, {"start": 1447.2, "end": 1447.32, "word": " N", "probability": 0.9775390625}, {"start": 1447.32, "end": 1447.56, "word": " ุฒุงุฆุฏ", "probability": 0.9388020833333334}, {"start": 1447.56, "end": 1448.44, "word": " ุชูุงุชุฉ", "probability": 0.9793701171875}, {"start": 1448.44, "end": 1448.58, "word": " ูู", "probability": 0.7158203125}, {"start": 1448.58, "end": 1448.9, "word": " ุชูุงุชุฉ", "probability": 0.9903564453125}, {"start": 1448.9, "end": 1449.02, "word": " N", "probability": 0.96728515625}, {"start": 1449.02, "end": 1449.2, "word": " ุฒุงุฆุฏ", "probability": 0.9581705729166666}, {"start": 1449.2, "end": 1449.42, "word": " ุงุชููู", "probability": 0.898193359375}, {"start": 1449.42, "end": 1449.56, "word": " ูู", "probability": 0.93359375}, {"start": 1449.56, "end": 1449.88, "word": " ุชูุงุชุฉ", "probability": 0.990966796875}, {"start": 1449.88, "end": 1449.98, "word": " N", "probability": 0.984375}, {"start": 1449.98, "end": 1450.42, "word": " ุฒุงุฆุฏ", "probability": 0.9723307291666666}, {"start": 1450.42, "end": 1450.82, "word": " ูุงุญุฏ", "probability": 0.98974609375}], "temperature": 1.0}, {"id": 63, "seek": 147289, "start": 1451.33, "end": 1472.89, "text": "ูุฃู ุฏุฑุฌุฉ ุงู bus 2 ูุฏุฑุฌุฉ ุงูู
ูุงู
3 ูุจุงูุชุงูู ุฏุฑุฌุฉ ุงู bus ุฃูู ู
ู ุฏุฑุฌุฉ ุงูู
ูุงู
ูุจูู limit ูุณุงูู ุณูุฑ ูุงูุณูุฑ ุฃูู ู
ู ุงููุงุญุฏ ูุจูู by the ratio test ุงู series ุชุจุนุชู converge ูุจุงูุชุงูู ู
ุฏุงู
ุงู series ุทูุนุช converge ุฅุฐุง ุงู summation ุงู series ุชุจุนุชูุง ุงูุฃุตููุฉ ุจุชููู converge absolutely", "tokens": [1211, 33456, 11778, 47341, 3660, 2423, 1255, 568, 4032, 3215, 47341, 3660, 9673, 4587, 10943, 805, 46599, 6027, 2655, 6027, 1829, 11778, 47341, 3660, 2423, 1255, 5551, 4587, 1211, 9154, 11778, 47341, 3660, 9673, 4587, 10943, 7251, 3555, 4587, 7578, 4948, 7251, 3794, 995, 45865, 8608, 5172, 2288, 16070, 3794, 5172, 2288, 5551, 4587, 1211, 9154, 2423, 14407, 24401, 7251, 3555, 4587, 7578, 538, 264, 8509, 1500, 2423, 2638, 6055, 3555, 3615, 31371, 41881, 46599, 6027, 2655, 6027, 1829, 3714, 3215, 10943, 2423, 2638, 23032, 1211, 34268, 41881, 11933, 15730, 2423, 28811, 2423, 2638, 6055, 3555, 34268, 8315, 16247, 36520, 10632, 39894, 30544, 41881, 3122], "avg_logprob": -0.2629717045797492, "compression_ratio": 1.9138755980861244, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1451.33, "end": 1451.71, "word": "ูุฃู", "probability": 0.696533203125}, {"start": 1451.71, "end": 1452.13, "word": " ุฏุฑุฌุฉ", "probability": 0.9842122395833334}, {"start": 1452.13, "end": 1452.29, "word": " ุงู", "probability": 0.6669921875}, {"start": 1452.29, "end": 1452.49, "word": " bus", "probability": 0.55126953125}, {"start": 1452.49, "end": 1453.11, "word": " 2", "probability": 0.0858154296875}, {"start": 1453.11, "end": 1453.75, "word": " ูุฏุฑุฌุฉ", "probability": 0.7933349609375}, {"start": 1453.75, "end": 1454.27, "word": " ุงูู
ูุงู
", "probability": 0.962890625}, {"start": 1454.27, "end": 1454.81, "word": " 3", "probability": 0.9150390625}, {"start": 1454.81, "end": 1455.77, "word": " ูุจุงูุชุงูู", "probability": 0.85341796875}, {"start": 1455.77, "end": 1456.13, "word": " ุฏุฑุฌุฉ", "probability": 0.9513346354166666}, {"start": 1456.13, "end": 1456.23, "word": " ุงู", "probability": 0.95703125}, {"start": 1456.23, "end": 1456.41, "word": " bus", "probability": 0.9609375}, {"start": 1456.41, "end": 1456.79, "word": " ุฃูู", "probability": 0.9322916666666666}, {"start": 1456.79, "end": 1456.93, "word": " ู
ู", "probability": 0.9775390625}, {"start": 1456.93, "end": 1457.25, "word": " ุฏุฑุฌุฉ", "probability": 0.9807942708333334}, {"start": 1457.25, "end": 1457.61, "word": " ุงูู
ูุงู
", "probability": 0.9793294270833334}, {"start": 1457.61, "end": 1457.85, "word": " ูุจูู", "probability": 0.873291015625}, {"start": 1457.85, "end": 1458.05, "word": " limit", "probability": 0.5322265625}, {"start": 1458.05, "end": 1458.61, "word": " ูุณุงูู", "probability": 0.77239990234375}, {"start": 1458.61, "end": 1459.11, "word": " ุณูุฑ", "probability": 0.6702677408854166}, {"start": 1459.11, "end": 1459.87, "word": " ูุงูุณูุฑ", "probability": 0.683990478515625}, {"start": 1459.87, "end": 1460.25, "word": " ุฃูู", "probability": 0.97509765625}, {"start": 1460.25, "end": 1460.49, "word": " ู
ู", "probability": 0.9931640625}, {"start": 1460.49, "end": 1461.07, "word": " ุงููุงุญุฏ", "probability": 0.7347005208333334}, {"start": 1461.07, "end": 1461.65, "word": " ูุจูู", "probability": 0.939697265625}, {"start": 1461.65, "end": 1461.87, "word": " by", "probability": 0.61669921875}, {"start": 1461.87, "end": 1462.11, "word": " the", "probability": 0.66650390625}, {"start": 1462.11, "end": 1462.39, "word": " ratio", "probability": 0.92919921875}, {"start": 1462.39, "end": 1462.79, "word": " test", "probability": 0.9296875}, {"start": 1462.79, "end": 1463.03, "word": " ุงู", "probability": 0.55322265625}, {"start": 1463.03, "end": 1463.27, "word": " series", "probability": 0.9296875}, {"start": 1463.27, "end": 1463.81, "word": " ุชุจุนุชู", "probability": 0.8682861328125}, {"start": 1463.81, "end": 1466.01, "word": " converge", "probability": 0.37353515625}, {"start": 1466.01, "end": 1467.03, "word": " ูุจุงูุชุงูู", "probability": 0.91171875}, {"start": 1467.03, "end": 1467.29, "word": " ู
ุฏุงู
", "probability": 0.5680338541666666}, {"start": 1467.29, "end": 1467.39, "word": " ุงู", "probability": 0.92626953125}, {"start": 1467.39, "end": 1467.57, "word": " series", "probability": 0.9326171875}, {"start": 1467.57, "end": 1467.87, "word": " ุทูุนุช", "probability": 0.7509765625}, {"start": 1467.87, "end": 1468.37, "word": " converge", "probability": 0.94384765625}, {"start": 1468.37, "end": 1469.03, "word": " ุฅุฐุง", "probability": 0.618896484375}, {"start": 1469.03, "end": 1469.19, "word": " ุงู", "probability": 0.818359375}, {"start": 1469.19, "end": 1469.59, "word": " summation", "probability": 0.94287109375}, {"start": 1469.59, "end": 1470.01, "word": " ุงู", "probability": 0.61865234375}, {"start": 1470.01, "end": 1470.23, "word": " series", "probability": 0.9404296875}, {"start": 1470.23, "end": 1470.59, "word": " ุชุจุนุชูุง", "probability": 0.74169921875}, {"start": 1470.59, "end": 1471.13, "word": " ุงูุฃุตููุฉ", "probability": 0.8621419270833334}, {"start": 1471.13, "end": 1471.51, "word": " ุจุชููู", "probability": 0.703369140625}, {"start": 1471.51, "end": 1472.03, "word": " converge", "probability": 0.95361328125}, {"start": 1472.03, "end": 1472.89, "word": " absolutely", "probability": 0.49560546875}], "temperature": 1.0}, {"id": 64, "seek": 149247, "start": 1475.77, "end": 1492.47, "text": "ุงูุงุฎุฑ ุดูุก ุจูุชุนุฑู ุนููู ุงูู Alternating P Series ุฒู ู
ุง ููู ุนูุฏูุง P Integral ููุงุฑููุง ุจ P Series ูููุง Alternating P Series ุงูุด ุงู Alternating P Seriesุ ุงููู ููุณ ุงู P Series ุจูุถูู ุนูููุง ููุต 1 ุฃุณู ุฃู ุฃุณู ุฒุงุฆุฏ ูุงุญุฏ ุทุจุนุง ุงู P ุฏุงุฆู
ุง ู
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ุง Converge ููู ูู ุนูุฏู ููุนูู ู
ู ุงู conversion ุชุจุนุชูุง ุฅุฐุง ูุงูุช ุงู P ุฃูุจุฑ ู
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ู ูุงุญุฏ ูุจูู converge ูุจูู ุงู absolutely converge ู
ุนูุงู ุฏุงูู ุฅูู ุงู summation ุนูู AN converge absolutely ูุจูู converge absolutely ุฅุฐุง ูุงูุช P ุฃูุจุฑ ู
ู ูุงุญุฏ ุญูู ุฎูุตูุง ู
ู ูุฐู ููู ุงู P series ูุฐู ุจุงู absolute value diverge ุฅุฐุง ูุงูุช ุงู P ุฃูู ุฃูู ุณูุงูุง ูุจูู ูู ูุฐู ุงูุญุงูุฉ test fair ุจู
ูุงุทู ุทุจู ุงูุชูุงุช ุดุฑูุท ุชูุงุช ุดุฑูุท ูู
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ูุฌุจุฉ ุงู UN' ูุงูุต P ุนูู N ุฃูุต P ุฒุงุฆุฏ ูุงุญุฏ ุณุงูุจ ูุจุงูุชุงูู ุงู UN decreasing ุงู limit ุชุจุนุชูุง ูุณุงูู ุณูุฑ ุฅุฐุง ุงูุชูุงุช ุงูุดุฑูุท ุงูุทุจูุช ูุจุงูุชุงูู ุงู series converged conditionally for P ุฃูู ุฃู ูุณุงูู ูุงุญุฏ ููุฐู ุงูู
ูู
ุฉ ุงู alternating P series ูุฅู ุนูู ุทูู ู
ู
ูู ุฃูุช ุชูุชุจู ุงูุฅุฌุงุจุฉ ุชุจุนุชูุง ูุจูู ูุฐู converged absolutely ูู ูุงูุช ุงู P ุฃูุจุฑ ู
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ุง ุจุชููู ash converge ููู ุฃููุงุน ุงู conversion ุชุจุนุชูุง ุนูู ุญุณุจ ููู
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