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

##### 1 Answer

Jan 30, 2017

the series is indeterminate.

#### Explanation:

We can easily see that the series is not convergent, since:

We can take a closer look at the partial sums:

and we can prove by induction that:

so that partial sums oscillate between the two values and do not converge to a limit.