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How to determine this infinite sum

  1. Mar 23, 2010 #1

    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

    Last edited: Mar 23, 2010
  2. jcsd
  3. Mar 23, 2010 #2


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    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).
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