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

##### 1 Answer

Feb 13, 2017

The alternating series:

is not convergent.

#### Explanation:

This is an alternating series so we can apply Leibniz's test stating that the series is convergent if given:

we have:

(i)

#lim_(n->oo) a_n = 0# (ii)

#a_(n+1)/a_n < 1#

Now consider the sequence:

We have:

And:

but as

The Leibniz's test is then not satisfied and the series is not convergent.