Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How to determine this infinite sum

  1. Mar 23, 2010 #1
    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. jcsd
  3. Mar 23, 2010 #2

    mathman

    User Avatar
    Science Advisor

    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).
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook