# Series Problem

• October 24th 2012, 03:38 PM
Preston019
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?
• October 24th 2012, 04:04 PM
Plato
Re: Series Problem
Quote:

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?
• October 24th 2012, 05:58 PM
Preston019
Re: Series Problem
Quote:

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?
• October 24th 2012, 07:12 PM
Prove It
Re: Series Problem
Yes, any series with terms that do not go to 0 is divergent.