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Консультация № 201540
24.10.2021, 15:41
0.00 руб.
1
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Здравствуйте! У меня возникли сложности с таким вопросом:Найти интервал сходимости степенного ряда. Исследовать поведение ряда на концах интервала сходимости.
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Обсуждение
25.10.2021, 19:16
общий
это ответ
Здравствуйте, Yulya!
Для решения задачи используем признак Даламбера:
Теперь определим, при каких значениях
этот предел меньше единицы: 
следовательно, 
В этом интервале заданный ряд сходится абсолютно.
При
имеем ряд 
который расходится как сравнимый с гармоническим рядом.
При
имеем ряд 
который условно сходится по признаку Лейбница.
Следовательно, интервал сходимости заданного ряда суть
Для решения задачи используем признак Даламбера:
Теперь определим, при каких значениях
этот предел меньше единицы: следовательно, В этом интервале заданный ряд сходится абсолютно.При
имеем ряд который расходится как сравнимый с гармоническим рядом.При
имеем ряд который условно сходится по признаку Лейбница.Следовательно, интервал сходимости заданного ряда суть
Об авторе:
Facta loquuntur.
Facta loquuntur.
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