# How to determine this infinite sum

1. Mar 23, 2010

### benf.stokes

Hi,

How do i determine de result in terms of x of this series:

(Sum(i=0..+infinity; i*x^i))/(Sum(i=0..+infinity;x^i)
For x<1

Thanks

Last edited: Mar 23, 2010
2. Mar 23, 2010

### mathman

The denominator is a simple geometric series = 1/(1-x). The numerator series can be gotten using elementary calculus from the denominator series = xd/dx(1/(1-x))=x/(1-x)^2.
Net result = x/(1-x).