Proving Divergence of Alternating Series with Limit Comparison Test

[Dell]

how do i prove that the following series diverges?

\sum(-1)^n-1*\frac{n-1}{n+1}*(1/\sqrt[n]{n})

is it enough to say that

lim {n->inf} \frac{n-1}{n+1}*(1/\sqrt[n]{n}) is not 0 ?


i know for regular series this would be okay but what about series with alternating signs??

how else can i tbe proven??

 

[Count Iblis]

Yes, an alternating series converges if and only if the limit of the terms go to zero.

 

[Dell]

thanks, youve really helped me with this work,