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Задать вопрос экспертам

Консультация № 177772

09.04.2010, 12:35

40.55 руб.

0 2 1

Образование

Здравствуйте! Помогите, пожалуйста, исследовать на сходимость ряд (по признаку Коши и, если возможно, поподробнее):

Спасибо!

Обсуждение

Неизвестный

09.04.2010, 14:47

общий

это ответ

Здравствуйте, MrSpencer.

Рассмотрим
lim_n->[$8734$]ⁿ[$8730$]((2+(-1)ⁿ)/2ⁿ)=(1/2)*lim_n->[$8734$]ⁿ[$8730$](2+(-1)ⁿ)
2+(-1)ⁿ[$8804$]3, для любых n
lim_n->[$8734$]ⁿ[$8730$]3=1
Получим
lim_n->[$8734$]ⁿ[$8730$]((2+(-1)ⁿ)/2ⁿ)[$8804$](1/2)*1
для любого d, 1/2<d<1 выполняется ⁿ[$8730$]((2+(-1)ⁿ)/2ⁿ) < d , следовательно
ряд [$8721$](2+(-1)ⁿ)/2ⁿ сходится по признаку Коши

5

давно

Посетитель
401481
7

31.03.2021, 12:37

общий

пожалуйста помогите решить. Сколько четырехзначных чисел можно образовать и цифр числа 1234567890000

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