# Convergence - Divergence of a Series

1. Apr 10, 2009

### remaan

1. The problem statement, all variables and given/known data
Test the series for convergence or divergence
-1/3+ 2/4 - 3/5 +4/6 - 5/7 + .................

2. Relevant equations

I think it's an alternating series

3. 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 ??

2. Apr 10, 2009

### latentcorpse

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 $n \rightarrow \infty$

3. Apr 11, 2009

### remaan

It will approach 1. and the series will Diverge.

What do you think ?