# Convergence - Divergence of a Series

## Homework Statement

Test the series for convergence or divergence
-1/3+ 2/4 - 3/5 +4/6 - 5/7 + .................

## Homework Equations

I think it's an alternating series

## The Attempt at a Solution

I found that an = (-1) ^n * n/ (n+2)

And it approaches 1 as n goes to inifty so the series will Diverge

Is that right ??

hmmm.
alternating series test says that if you can identify a series of the form $\sum (-1)^n a_n$ and the $a_n$ are positive and decreasing such that $a_n \rightarrow 0$ then $\sum (-1)^n a_n$ will converge.

so here you have $a_n=\frac{n}{n+2}=\frac{1}{1+\frac{2}{n}}$

how does this behave as $n \rightarrow \infty$

It will approach 1. and the series will Diverge.

What do you think ?