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Forumla for its partial sum

  1. Nov 27, 2007 #1
    I've been asked to show that the series:

    http://img260.imageshack.us/img260/2676/asdaam0.jpg

    That it telescopes, hence find a forumla for its partial sum, and then state the limit.

    I'm sure I could find a formula for its partial sum IF I could simply show that it telescopes, for me I can't see how it does. Maybe I have a wrong definition of telescoping, but I thought it was when the majority of terms cancel, where in that series I can't see happening. Also I believe from inspection the limit is (ln 1).

    Any help? :)

    Thanks
     
  2. jcsd
  3. Nov 27, 2007 #2

    Avodyne

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    Science Advisor

    It might help to notice that 1-1/k^2 = (k+1)(k-1)/k^2.
     
  4. Nov 28, 2007 #3
    Yeah they gave us that as a hint. I can't see how it helps though :P
     
  5. Nov 28, 2007 #4

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    So
    [tex]ln(1-\frac{2}{k^2})= ln(\frac{(k-1)(k+1)}{k^2}[/tex]
    What is THAT equal to?
     
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