# How to prove the following:

1. Apr 19, 2009

### 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??

2. Apr 19, 2009

### Count Iblis

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

3. Apr 19, 2009

### Dell

thanks, youve really helped me with this work,