Determining Convergence of Alternative Series

[quasar987]

Leibniz criterion for alterning serie say that if the two conditons a_n >0 is decreasing and -->0 are satisfied, the serie converges. It doesn't say that if they don't it diverge.

So how do you determine the convergence of an alternative serie that doesn't satisfy the conditions? For exemple,

\sum_{n=1}^{\infty} (-1)^n\frac{1}{n^{1/n}}

a_n \rightarrow 1 \neq 0

 

[Hurkyl]

So, you're asking what test to use when the terms don't converge to 0?

 

[quasar987]

Yeah, a test, ok.. maybe I should have tought about this one a little longer. :/