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Homework Help: Question on summing

  1. May 4, 2010 #1
    1. The problem statement, all variables and given/known data
    Find the sum of the series:
    [tex]\sum^{\infty}_{n=3}\frac{1}{(2n-3)(2n-1)}[/tex]
    2. Relevant equations
    N/A
    3. The attempt at a solution
    This isn't geometric, I can't get it from any common Maclaurin series (as far as I can work out). The book I have tells me the answer is 1/6, I'm sure I'm doing something stupid. Thanks in advance for any help!
     
  2. jcsd
  3. May 4, 2010 #2

    Mark44

    Staff: Mentor

    Try breaking up the summand using partial fraction decomposition, and then expand the series.
     
  4. May 4, 2010 #3
    OK, so I have [tex]\sum^{\infty}_{n=3}\frac{1}{2(2n-3)}-\frac{1}{2(2n-1)}[/tex], but I'm not sure what you mean by "expanding the series"; should I split it into two summations? And if so, where do I go from there?
     
  5. May 4, 2010 #4

    Mark44

    Staff: Mentor

    No, not two series - just one. Expanding the series means writing out the sum of terms, starting with the one for n = 3. Look at the sequence of partial sums, Sk, the sum of the terms from n = 3 to n = k.
     
  6. May 4, 2010 #5
    *hits self in head* Wow! Thanks a ton, that should have been obvious.
     
  7. May 4, 2010 #6

    Mark44

    Staff: Mentor

    These things are obvious only after you have done them a time or two.
     
  8. May 4, 2010 #7
    Yah, well at least now when I see it again I'll know what to do! Thanks again for the help.
     
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