# Homework Help: Sum of Series

1. Feb 20, 2008

### Spark15243

1. The problem statement, all variables and given/known data

Find the sum of the series.

Summation (n/2^n)
from n = 1 to inf

2. Relevant equations

Summation (x^n) = 1/1-x

3. The attempt at a solution

n/2^n
n*(1/2)^n

Not sure what this equals after this... I was thinking (1/1-0.5) but that is a guess.
There are other ones like this, i have no idea how to do them, so any help on how to start and/or finish them will be appreciated.

2. Feb 20, 2008

### quasar987

Have you covered uniform convergence of series?

3. Feb 20, 2008

### Spark15243

I...don't know. Ik that the terms themselves converge to zero, but I dont know how to calc the sum...

4. Feb 20, 2008

### Dick

Differentiate Summation(x^n)=1/(1-x). Put x=1/2.

5. Feb 21, 2008

### quasar987

This is what I had in mind, but don't we need uniform convergence to justify differentiating under the sum?

I remember doing this problem w/o this trick a year ago. It involved rearanging the series if my memory serves me right.

6. Feb 21, 2008

### Spark15243

What do I do about the extra n in front then?