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Консультация № 190758
21.03.2017, 09:32
0.00 руб.
21.03.2017, 10:05
1
3
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Найти интервал сходимости ряда
Найти интервал сходимости ряда
Прикрепленные файлы:
Обсуждение
21.03.2017, 09:53
общий
Адресаты:
Наверное, нужно не "найти сходимость", а "найти интервал сходимости"? Уточните задание.
Об авторе:
Facta loquuntur.
Facta loquuntur.
21.03.2017, 11:50
общий
это ответ
Здравствуйте, maksim-maksimka-2015!
Имеем
Используем признак Даламбера:
Вычислим, когда этот предел меньше единицы:
В этом интервале заданный ряд сходится абсолютно. При
и 
ряд расходится.
Исследуем поведение ряда в граничных точках. Если
то получим сходящийся числовой ряд 
(он сравним со сходящимся рядом 
). Если 
то получим знакочередующийся числовой ряд 
который сходится по признаку Лейбница.
Значит, ряд сходится в интервале
Имеем
Используем признак Даламбера:Вычислим, когда этот предел меньше единицы:
В этом интервале заданный ряд сходится абсолютно. При
и ряд расходится.Исследуем поведение ряда в граничных точках. Если
то получим сходящийся числовой ряд (он сравним со сходящимся рядом ). Если то получим знакочередующийся числовой ряд который сходится по признаку Лейбница.Значит, ряд сходится в интервале
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
Форма ответа
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