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Консультация № 198872
08.06.2020, 15:40
0.00 руб.
1
1
1
Здравствуйте! Прошу помощи в следующем вопросе:
Найти область сходимости ряда
Найти область сходимости ряда
Прикрепленные файлы:
Обсуждение
17.07.2022, 09:25
общий
это ответ
Здравствуйте, Наталья!
Используя признак Даламбера, получим
Определим, при каких значениях
этот предел меньше единицы: 
В этом промежутке заданный ряд сходится абсолютно.
При
получим числовой ряд 
который сходится как ряд Дирихле с показателем степени 
При
получим знакочередующийся числовой ряд 
который абсолютно сходится согласно признаку Лейбница и указанной выше сходимости ряда 
Следовательно, областью сходимости заданного ряда является промежуток
Используя признак Даламбера, получим
Определим, при каких значениях
этот предел меньше единицы: В этом промежутке заданный ряд сходится абсолютно.При
получим числовой ряд который сходится как ряд Дирихле с показателем степени При
получим знакочередующийся числовой ряд который абсолютно сходится согласно признаку Лейбница и указанной выше сходимости ряда Следовательно, областью сходимости заданного ряда является промежуток
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
Форма ответа
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