1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Infinite series in terms of x

  1. Mar 23, 2010 #1
    1. The problem statement, all variables and given/known data

    Hi,

    How do i determine de result in terms of x of this series for x < 1:

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

    Thanks


    3. The attempt at a solution

    I know that (Sum(i=0..+infinity;x^i) will tend do 1/(1-x) but i don't know what the numerator will tend to

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

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Hi benf.stokes! :smile:

    (have a sigma: ∑ and an infinity: ∞ and try using the X2 and X2 tags just above the Reply box :wink:)
    Hint: integrate. :smile:
     
  4. Mar 29, 2010 #3
    Thanks, I figured it out but by differentiating (sorry for the delay but I was netless for a few days):

    [tex]
    \sum_{n=0}^{\infty}x^n=\frac{1}{1-x}
    [/tex]

    [tex]
    \sum_{n=0}^{\infty}nx^{n-1}=\frac{1}{(1-x)^2}
    [/tex]

    [tex]
    \sum_{n=0}^{\infty}nx^n=\frac{x}{(1-x)^2}
    [/tex]

    How would it be done by integrating? The other way around?
     
    Last edited: Mar 29, 2010
  5. Mar 29, 2010 #4

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Sum the integral, and then differentiate that sum. :smile:
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook