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Консультация № 197419
14.12.2019, 18:18
0.00 руб.
14.12.2019, 21:48
0
1
1
Здравствуйте! Прошу помощи в следующем вопросе:
Обсуждение
19.12.2019, 18:49
общий
это ответ
Здравствуйте, Алиса!
Для данного ряда
Согласно признаку Даламбера, ряд сходится при [$961$]<1 и расходится при [$961$]>1 (при [$961$]=1 вопрос о сходимости ряда рассматривается особо). В данном случае из [$961$] = 10|x| < 1 следует |x| < 1/10, то есть ряд сходится при -1/10 < x < 1/10 и расходится при x < -1/10 и при x > 1/10. При x = 1/10 получаем ряд 1 + 1 + 1 + ..., который, очевидно, расходится. При x = -1/10 получаем знакочередующийся ряд -1 + 1 - 1 + ..., сумма которого не имеет предела, следовательно, он также расходится.
Итак, интервал сходимости ряда - (-1/10, 1/10).
Для данного ряда
Согласно признаку Даламбера, ряд сходится при [$961$]<1 и расходится при [$961$]>1 (при [$961$]=1 вопрос о сходимости ряда рассматривается особо). В данном случае из [$961$] = 10|x| < 1 следует |x| < 1/10, то есть ряд сходится при -1/10 < x < 1/10 и расходится при x < -1/10 и при x > 1/10. При x = 1/10 получаем ряд 1 + 1 + 1 + ..., который, очевидно, расходится. При x = -1/10 получаем знакочередующийся ряд -1 + 1 - 1 + ..., сумма которого не имеет предела, следовательно, он также расходится.
Итак, интервал сходимости ряда - (-1/10, 1/10).
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