How to determine this infinite sum

  • #1

Main Question or Discussion Point

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:

Answers and Replies

  • #2
mathman
Science Advisor
7,759
415
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).
 

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