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Консультация № 201224
27.06.2021, 08:58
0.00 руб.
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Здравствуйте! Прошу помощи в следующем вопросе:
Исследовать на абсолютную и условную сходимость знакочередующийся ряд
Исследовать на абсолютную и условную сходимость знакочередующийся ряд
Прикрепленные файлы:
Обсуждение
27.06.2021, 18:32
общий
это ответ
Здравствуйте, oligator.a.y!
Рассмотрим сначала ряд
который составлен из абсолютных величин членов заданного ряда. Сравним его с расходящимся рядом 
при 
-- конечное число, не равное нулю. Значит, ряд
тоже расходится. Поэтому у заданного знакочередующегося ряда нет абсолютной сходимости.
Применим к заданному ряду признак Лейбница:
1) при 
2)
Оба условия признака Лейбница выполнены. Значит, заданный ряд сходится условно.
Рассмотрим сначала ряд
который составлен из абсолютных величин членов заданного ряда. Сравним его с расходящимся рядом при -- конечное число, не равное нулю. Значит, ряд
тоже расходится. Поэтому у заданного знакочередующегося ряда нет абсолютной сходимости.Применим к заданному ряду признак Лейбница:
1) при
2)
Оба условия признака Лейбница выполнены. Значит, заданный ряд сходится условно.
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
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