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Консультация № 190753
20.03.2017, 13:11
0.00 руб.
20.03.2017, 14:31
1
1
1
Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
помогите найти интервал сходимости ряда
помогите найти интервал сходимости ряда
Прикрепленные файлы:
Обсуждение
20.03.2017, 14:11
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 
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 Если то получим знакочередующийся числовой ряд который сходится по признаку Лейбница.Значит, ряд сходится в интервале
Об авторе:
Facta loquuntur.
Facta loquuntur.
Форма ответа
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