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Math Help - General formula of a series

  1. #1
    Newbie
    Joined
    Jul 2010
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    9

    Post General formula of a series

    Hi everyone! I have some problems in understanding the following general formula:
    \displaystyle S_n=\sum_{k=2}^{n} \frac{1}{k^2-1}=\frac{3}{4}-\frac{1}{2n}-\frac{1}{2(n+1)}
    Does anyone have a proof for this? Any effort will be appreciated.
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  2. #2
    Junior Member
    Joined
    Nov 2009
    Posts
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    Replace  \frac{1}{k^2-1} with its partial fraction decomposition, then write out the series term by term. A bunch of stuff should cancel leaving the desired result.
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