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Math Help - finding the convergent value of an infinite sum

  1. #1
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    finding the convergent value of an infinite sum

    finding the convergent value of an infinite sum-image-1-.png

    I'm not sure how to evaluate this

    33/4 is the right answer but how do I get there?

    Using fractional decomposition I get finding the convergent value of an infinite sum-image-2-.png

    And that gives a telescoping sum of finding the convergent value of an infinite sum-image-3-.png

    where do I go from here?
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  2. #2
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    Re: finding the convergent value of an infinite sum

    Hi,
    Consider the following:

    Last edited by johng; June 29th 2014 at 04:43 PM.
    Thanks from kingsolomonsgrave
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  3. #3
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    Re: finding the convergent value of an infinite sum

    I think so, everything cancels but for the 1 and the 1/2 at the beginning and the last term 1/n+2 which goes to zero as n goes to infinity. Therefore you get 11/2 times (1+1/2) which is (11/2)(3/2) = 33/4
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