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Консультация № 191125
11.06.2017, 08:25
0.00 руб.
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Здравствуйте! У меня возникли сложности с таким вопросом:
Прикрепленные файлы:
Обсуждение
11.06.2017, 12:03
общий
это ответ
Здравствуйте, asdf1234!
Используем признак Даламбера:
и определяем, при каких значениях
этот предел меньше единицы: 
В этом интервале ряд сходится абсолютно. Вне этого интервала ряд расходится.
Исследуем сходимость ряда в граничных точках интервала.
При
имеем ряд 
который расходится как сравнимый с гармоническим рядом 
При
имеем знакочередующийся ряд 
который сходится по признаку Лейбница.
Следовательно, заданный ряд сходится в интервале
Используем признак Даламбера:
и определяем, при каких значениях
этот предел меньше единицы: В этом интервале ряд сходится абсолютно. Вне этого интервала ряд расходится.Исследуем сходимость ряда в граничных точках интервала.
При
имеем ряд который расходится как сравнимый с гармоническим рядом При
имеем знакочередующийся ряд который сходится по признаку Лейбница.Следовательно, заданный ряд сходится в интервале
Об авторе:
Facta loquuntur.
Facta loquuntur.
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