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Консультация № 197422
14.12.2019, 18:20
0.00 руб.
14.12.2019, 21:24
0
1
1
Здравствуйте! Прошу помощи в следующем вопросе:
Обсуждение
20.12.2019, 04:27
общий
это ответ
Здравствуйте, Алиса!
Воспользуемся признаком Даламбера: если существует предел
то ряд [$8721$]a[sub]n[/sub] сходится при [$961$]<1 и расходится при [$961$]>1 (при [$961$]=1 сходимость ряда нужно исследовать особо). В данном случае
Из [$961$] = |x|/10 <1 следует, что ряд сходится при -10 < x < 10 и расходится при x < -10 и при x > 10. При x = 10 получаем расходящийся ряд
(так называемый гармонический ряд). При x = -10 имеем знакочередующийся ряд
который является сходящимся по признаку Лейбница (последовательность его членов монотонно убывает и стремится к нулю). Следовательно, исходный функциональный ряд сходится на полуинтервале [-10, 10) (то есть правильный ответ - C).
Воспользуемся признаком Даламбера: если существует предел
то ряд [$8721$]a[sub]n[/sub] сходится при [$961$]<1 и расходится при [$961$]>1 (при [$961$]=1 сходимость ряда нужно исследовать особо). В данном случае
Из [$961$] = |x|/10 <1 следует, что ряд сходится при -10 < x < 10 и расходится при x < -10 и при x > 10. При x = 10 получаем расходящийся ряд
(так называемый гармонический ряд). При x = -10 имеем знакочередующийся ряд
который является сходящимся по признаку Лейбница (последовательность его членов монотонно убывает и стремится к нулю). Следовательно, исходный функциональный ряд сходится на полуинтервале [-10, 10) (то есть правильный ответ - C).
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