1. ## Series Problem

How do you find the sum of sum from n=0 to infinity of (n(-2)^n)/(2^n).

Do I use alternating series test and geometric series?

2. ## Re: Series Problem

Originally Posted by Preston019
How do you find the sum of sum from n=0 to infinity of (n(-2)^n)/(2^n).
Do I use alternating series test and geometric series?
Note that $(-2)^n=(-1)^n2^n$ so $n\frac{(-2)^n}{2^n}=(-1)^nn$
So what?

3. ## Re: Series Problem

Originally Posted by Plato
Note that $(-2)^n=(-1)^n2^n$ so $n\frac{(-2)^n}{2^n}=(-1)^nn$
So what?
It's divergent, right?

4. ## Re: Series Problem

Yes, any series with terms that do not go to 0 is divergent.