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Консультация № 197420
14.12.2019, 18:19
0.00 руб.
14.12.2019, 21:45
0
1
1
Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Обсуждение
20.12.2019, 03:56
общий
это ответ
Здравствуйте, Алиса!
Рассмотрим ряд, составленный из абсолютных значений членов исходного ряда:
Воспользуемся интегральным признаком сходимости: если имеется непрерывная убывающая функция f(x) и последовательность a[sub]k[/sub] = f(k), k=1,2,3,..., то ряд
и интеграл
одновременно сходятся, либо расходятся. В данном случае f(x) = 1/x[sup]3[/sup], и так как интеграл
сходится, то сходится и ряд
а значит исходный ряд
сходится абсолютно.
Рассмотрим ряд, составленный из абсолютных значений членов исходного ряда:
Воспользуемся интегральным признаком сходимости: если имеется непрерывная убывающая функция f(x) и последовательность a[sub]k[/sub] = f(k), k=1,2,3,..., то ряд
и интеграл
одновременно сходятся, либо расходятся. В данном случае f(x) = 1/x[sup]3[/sup], и так как интеграл
сходится, то сходится и ряд
а значит исходный ряд
сходится абсолютно.
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