# How do you test the alternating series #Sigma (n(-1)^(n+1))/lnn# from n is #[2,oo)# for convergence?

##### 1 Answer

Mar 9, 2017

The series:

is not convergent.

#### Explanation:

A necessary condition for any series to converge is that:

which also implies:

In our case:

so the series is not convergent.

We can also see that taking only the terms of even order:

while for terms of odd order:

so the series is irregular.