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Консультация № 198847
04.06.2020, 19:15
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Как исследовать на абсолютную и условную сходимость знакочередующийся ряд
∑_(n=1)^∞▒〖(-1)ⁿ 1/(2n-1)3ⁿ〗
Как исследовать на абсолютную и условную сходимость знакочередующийся ряд
∑_(n=1)^∞▒〖(-1)ⁿ 1/(2n-1)3ⁿ〗
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Обсуждение
18.07.2022, 06:28
общий
это ответ
Здравствуйте, master87!
Знакоположительный ряд
образован членами убывающей геометрической прогрессии и сходится. Каждый член этого ряда, начиная со второго, больше соответствующего члена знакоположительного ряда 
который составлен из модулей членов заданного ряда. Значит, этот ряд тоже сходится. Поскольку заданный ряд удовлетворяет условиям признака Лейбница сходимости знакочередующихся рядов, постольку, с учётом изложенного выше, он абсолютно сходится.
Знакоположительный ряд
образован членами убывающей геометрической прогрессии и сходится. Каждый член этого ряда, начиная со второго, больше соответствующего члена знакоположительного ряда который составлен из модулей членов заданного ряда. Значит, этот ряд тоже сходится. Поскольку заданный ряд удовлетворяет условиям признака Лейбница сходимости знакочередующихся рядов, постольку, с учётом изложенного выше, он абсолютно сходится.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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