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Консультация № 198877
08.06.2020, 22:36
0.00 руб.
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Исследовать на абсолютную и условную сходимость знакочередующийся ряд
Исследовать на абсолютную и условную сходимость знакочередующийся ряд
Прикрепленные файлы:
Обсуждение
13.06.2020, 16:29
общий
это ответ
Здравствуйте, Людмила!
Для ряда
составленного из абсолютных значений членов исходного ряда, воспользуемся признаком Даламбера: если существует предел
то ряд
сходится при [$961$]<1 и расходится при [$961$]>1 (при [$961$]=1 ряд может как сходиться, так и расходиться). В данном случае
и
следовательно, ряд сходится, то есть исходный ряд сходится абсолютно, следовательно, является и сходящимся (не условно).
Для ряда
составленного из абсолютных значений членов исходного ряда, воспользуемся признаком Даламбера: если существует предел
то ряд
сходится при [$961$]<1 и расходится при [$961$]>1 (при [$961$]=1 ряд может как сходиться, так и расходиться). В данном случае
и
следовательно, ряд сходится, то есть исходный ряд сходится абсолютно, следовательно, является и сходящимся (не условно).
5
Большое спасибо за ответ!
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