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Консультация № 170394
13.07.2009, 09:16
0.00 руб.
0
1
1
Исследовать на сходимость знакопостоянный ряд:
[$8721$](n=1...[$8734$])(n2+1)/[$8730$](n6+n5-1)
[$8721$](n=1...[$8734$])(n2+1)/[$8730$](n6+n5-1)
Обсуждение
Неизвестный
13.07.2009, 13:00
общий
это ответ
Здравствуйте, Alik4546.
Применим предельный признак сравнения, сравнив даннный ряд с расходящимся гармоническим рядом ∑(n=1...∞) 1/n. Так как предел отношения общих членов двух рядов
lim (n->oo) un/vn = lim (n->oo) {(n2+1)/√(n6+n5-1) : 1/n} =
= lim (n->oo) (n3+n)/√(n6+n5-1) = lim (n->oo) (1+1/n2)/√(1+1/n-1/n6) = 1 есть конечное число, не равное нулю, то данный ряд, так же как и эталонный гармонический, расходится.
Применим предельный признак сравнения, сравнив даннный ряд с расходящимся гармоническим рядом ∑(n=1...∞) 1/n. Так как предел отношения общих членов двух рядов
lim (n->oo) un/vn = lim (n->oo) {(n2+1)/√(n6+n5-1) : 1/n} =
= lim (n->oo) (n3+n)/√(n6+n5-1) = lim (n->oo) (1+1/n2)/√(1+1/n-1/n6) = 1 есть конечное число, не равное нулю, то данный ряд, так же как и эталонный гармонический, расходится.
5
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