Thread: Help 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..)

Originally Posted by nappysnake

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 :/

Use the alternating series test (1/2 + 1/k)^k is monotone decreasing after a a certain value of n ....)

The ratio test will work too. By the ratio test, the series will be convergent if



So the series converges.

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?

Originally Posted by nappysnake

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..)

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)



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