# How do you test the alternating series #Sigma (-1)^n(2^n+1)/(3^n-2)# from n is #[0,oo)# for convergence?

##### 1 Answer

Jan 26, 2017

The series is convergent.

#### Explanation:

A sufficient condition for an alternating series to converge is established by the Leibniz test stating that if:

(i)

(ii)

then the series is convergent.

In our case:

so the first condition is satisfied.

Now consider:

clearly:

and:

so that:

and it follows that:

Thus also the second condition is satisfied and the series os convergent.