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Консультация № 189837
02.10.2016, 21:33
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Здравствуйте! У меня возникли сложности с таким вопросом:
Обсуждение
02.10.2016, 21:35
общий
Вы решили выложить все задания с контрольной, чтобы Вам ее решили?
Какие именно трудности возникли в решении? Покажите свои наброски
Какие именно трудности возникли в решении? Покажите свои наброски
05.10.2016, 20:33
общий
это ответ
Здравствуйте, d28597!
Учитывая, что по техническим причинам функциональность портала нарушена, промежуточные выкладки опускаю. Вам предстоит восстановить их самостоятельно.
Применим к заданному ряду признак Даламбера:
Если -3<x<3, то D<1, и заданный ряд сходится абсолютно. Если x=3, то рассматриваемый ряд имеет вид [sub]n=1[/sub][$8721$][sup][$8734$][/sup]1/(n+3) и расходится как сравнимый с расходящимся гармоническим рядом. Если x=-3, то рассматриваемый ряд имеет вид [sub]n=1[/sub][$8721$][sup][$8734$][/sup](-1)[sup]n[/sup]/(n+3) и сходится условно по признаку Лейбница.
Учитывая, что по техническим причинам функциональность портала нарушена, промежуточные выкладки опускаю. Вам предстоит восстановить их самостоятельно.
Применим к заданному ряду признак Даламбера:
D=lim[sub]n[$8594$][$8734$][/sub]|a[sub]n+1[/sub]/a[sub]n[/sub]|=lim[sub]n[$8594$][$8734$][/sub]|x/3|.
Если -3<x<3, то D<1, и заданный ряд сходится абсолютно. Если x=3, то рассматриваемый ряд имеет вид [sub]n=1[/sub][$8721$][sup][$8734$][/sup]1/(n+3) и расходится как сравнимый с расходящимся гармоническим рядом. Если x=-3, то рассматриваемый ряд имеет вид [sub]n=1[/sub][$8721$][sup][$8734$][/sup](-1)[sup]n[/sup]/(n+3) и сходится условно по признаку Лейбница.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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