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Sum to the infinity of a series

  1. Jul 15, 2012 #1
    1. The problem statement, all variables and given/known data

    to find the value of [itex]\sum[/itex] over n=1 to ∞ of [1/{1+(n-1)2}](1/3)[itex]^{2+(n-1)2}[/itex]

    2. Relevant equations



    3. The attempt at a solution
    I have tried to solve in the way the arithmetico-geometric series are solved and tried to bring it in the form of the expansion of ln(1+y), because the answer has logarithmic term in it.
     
  2. jcsd
  3. Jul 15, 2012 #2

    Curious3141

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    Homework Helper

    Hints:

    Get rid of the (n-1) by starting the sum off from n = 0, that'll make things clearer.

    Observe that [itex]{(\frac{1}{3})}^{2 + 2n} =\frac{1}{3}.{(\frac{1}{3})}^{2n + 1}[/itex]

    What's [itex]\int_0^x t^{2n} dt[/itex]?
     
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