Finding the Sum of a Series: n/2^n

[Spark15243]

Homework Statement

Find the sum of the series.

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

Homework Equations

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

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.

 

[quasar987]

Have you covered uniform convergence of series?

 

[Spark15243]

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

 

[Dick]

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

 

[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.

 

[Spark15243]

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