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Консультация № 196839
27.10.2019, 13:35
0.00 руб.
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Здравствуйте! У меня возникли сложности с таким вопросом:
Прикрепленные файлы:
Обсуждение
03.08.2022, 09:31
общий
это ответ
Здравствуйте, li.a!
Используем признак Даламбера:
Определим, при каких значениях
этот предел меньше единицы: 
В этом промежутке ряд сходится абсолютно.
При
получим ряд 
который сходится как ряд Дирихле, или обобщённый гармонический ряд, с показателем степени 
При
получим знакочередующийся ряд 
который абсолютно сходится, потому что он удовлетворяет признаку Лейбница и сходится ряд, составленный из модулей его членов, который рассмотрен выше.
Следовательно, областью сходимости заданного ряда является промежуток
На всём промежутке ряд сходится абсолютно.
Используем признак Даламбера:
Определим, при каких значениях
этот предел меньше единицы: В этом промежутке ряд сходится абсолютно.При
получим ряд который сходится как ряд Дирихле, или обобщённый гармонический ряд, с показателем степени При
получим знакочередующийся ряд который абсолютно сходится, потому что он удовлетворяет признаку Лейбница и сходится ряд, составленный из модулей его членов, который рассмотрен выше.Следовательно, областью сходимости заданного ряда является промежуток
На всём промежутке ряд сходится абсолютно.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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