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Консультация № 201668
13.11.2021, 07:09
0.00 руб.
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Здравствуйте! У меня возникли сложности с таким вопросом:
Найти область сходимости
Найти область сходимости
Обсуждение
15.11.2021, 19:43
общий
это ответ
Здравствуйте, Александр!
Обозначим
и определим область сходимости степенного ряда 
Используя признак Д'Аламбера, получим
Последний предел меньше единицы при
то есть при 
или 
В этом промежутке заданный ряд сходится абсолютно.
Исследуем сходимость заданного ряда на концах промежутка сходимости. При
имеем ряд 
который сходится как сравнимый со сходящимся рядом 
При 
имеем знакочередующийся ряд 
который абсолютно сходится в силу сходимости предыдущего ряда.
Следовательно, заданный ряд сходится на отрезке
Обозначим
и определим область сходимости степенного ряда Используя признак Д'Аламбера, получимПоследний предел меньше единицы при
то есть при или В этом промежутке заданный ряд сходится абсолютно.Исследуем сходимость заданного ряда на концах промежутка сходимости. При
имеем ряд который сходится как сравнимый со сходящимся рядом При имеем знакочередующийся ряд который абсолютно сходится в силу сходимости предыдущего ряда.Следовательно, заданный ряд сходится на отрезке
Об авторе:
Facta loquuntur.
Facta loquuntur.
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