# Leibniz test

1. Dec 9, 2004

### 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,

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

$$a_n \rightarrow 1 \neq 0$$

2. Dec 9, 2004

### Hurkyl

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

3. Dec 9, 2004