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Find The Sum Of The Convergent Series

  1. Oct 4, 2012 #1
    1. The problem statement, all variables and given/known data
    [itex]\sum_{n=2}^{\infty} \frac{1}{n^2-1}[/itex]


    2. Relevant equations



    3. The attempt at a solution
    After doing partial fraction decomposition, I discovered that it was a telescoping series of some sort; the partial sum being 1/2[ (1 -1/3) + (1/2 - 1/4) + (1/3 - 1/4) +....] The only thing I can't do is see the pattern to make a nth partial sum. How would I go about this?
     
  2. jcsd
  3. Oct 4, 2012 #2

    vela

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    Write out the first few partial sums explicitly. Four or five is probably enough to see how the cancellations work out and which terms are going to stick around.
     
  4. Oct 4, 2012 #3
    Well, I can see that the 1 and 1/2 would have nothing to cancel out with; but what I can truly see doesn't go beyond that.
     
  5. Oct 4, 2012 #4

    vela

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    What specifically is confusing you? Frankly, I don't see how you can not see the pattern after writing out the first handful of partial sums.
     
  6. Oct 4, 2012 #5
    I attached the solution from the text-book. I don't understand how they get 1/n in the simplified nth partial sum formula.
     

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