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Консультация № 203125
03.09.2022, 20:59
0.00 руб.
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Здравствуйте! У меня возникли сложности с таким вопросом: Иследовать сходимость знакопеременного ряда ?
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Обсуждение
04.09.2022, 06:38
общий
это ответ
Здравствуйте, mavrin-mpo!
Пусть требуется исследовать сходимость знакопеременного ряда
Рассмотрим сначала ряд, который составлен из абсолютных величин членов заданного, то есть ряд
Проверим, выполняется ли для него необходимое условие сходимости:
Указанный предел не равен нулю. Поэтому ряд, который составлен из абсолютных величин членов заданного, расходится. Тогда расходится и заданный ряд, потому что он не удовлетворяет признаку Лейбница (общий член не стремится к нулю).
Пусть требуется исследовать сходимость знакопеременного ряда
Рассмотрим сначала ряд, который составлен из абсолютных величин членов заданного, то есть ряд
Проверим, выполняется ли для него необходимое условие сходимости:Указанный предел не равен нулю. Поэтому ряд, который составлен из абсолютных величин членов заданного, расходится. Тогда расходится и заданный ряд, потому что он не удовлетворяет признаку Лейбница (общий член не стремится к нулю).
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Об авторе:
Facta loquuntur.
Facta loquuntur.
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