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Finding the sum of an infinite series

  1. Mar 14, 2010 #1
    1. The problem statement, all variables and given/known data
    [tex]\sum\frac{1}{n2^(n+1)}[/tex] from 1 to infinity.

    By the way, that 2 is to the power of (n+1), doesn't show clearly.

    2. Relevant equations
    3. The attempt at a solution
    I have worked out the first few individual calculations, up to n=6, and i know it approaches ln(2)/2, however I have no idea how to actually prove this.
     
  2. jcsd
  3. Mar 14, 2010 #2

    jbunniii

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    What sorts of theorems do you know about power series?
     
  4. Mar 14, 2010 #3
    A few, it's for a 2nd year university subject. We've been using proof by induction a fair bit, but other than that I don't know the actual names for them.
     
  5. Mar 14, 2010 #4
    What do you know of integrating power series?
     
  6. Mar 14, 2010 #5
    You mean int(1 + x + x^2 + x^3 + ...) = x + x^2/2 + x^3/3 + ... ?
     
  7. Mar 14, 2010 #6

    jbunniii

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    Yes. See if you can work out how to apply that property to your problem.

    (Hint: start by replacing the "1/2" with a variable.)

    By the way, you can click on the following equation if you want to see how to typeset the sum properly:

    [tex]\sum_{n=1}^{\infty}\frac{1}{n 2^{n+1}}[/tex]
     
    Last edited: Mar 14, 2010
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