I have a series and i have a problem doing the ratio test....

Σ k=1 to infinity, (-1)^k (1/2 + 1/k)^k

i face my problem with the 1/k :/

edit: (i have to actually examine the absolute convergence and i think i have to first examine the ratio..)

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- December 6th 2011, 11:50 AMnappysnakeHelp about ratio test for series..
I have a series and i have a problem doing the ratio test....

Σ k=1 to infinity, (-1)^k (1/2 + 1/k)^k

i face my problem with the 1/k :/

edit: (i have to actually examine the absolute convergence and i think i have to first examine the ratio..) - December 6th 2011, 12:02 PMmr fantasticRe: Help about ratio test for series..
- December 6th 2011, 04:36 PMProve ItRe: Help about ratio test for series..
The ratio test will work too. By the ratio test, the series will be convergent if

So the series converges. - December 18th 2011, 12:21 AMnappysnakeRe: Help about ratio test for series..
i have one further question. how would you calculate absolute convergence? wolfram alpha says that the ratio test is conclusive and that the series converges, but i have no idea how he comes to the result..all i get is a bunch of terms which i can't simplify..help?

- December 18th 2011, 01:31 AMchisigmaRe: Help about ratio test for series..
It is difficult to undestand why it is requested the ratio test instead of the root test, that extablishes that a series converges if...

(1)

In that case is...

(2)

http://www.sv-luka.org/ikone/ikone180a.jpg

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