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Math Help - Sum of a finite series

  1. #1
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    Sum of a finite series

    For a fixed + integer k, what is the general formula for the finite series SUM j=1 to n of [(-1)^j][ j^k] ?
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  2. #2
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    This is not an easy question.

    Without the (-1)^j you can find the answer Summation - Wikipedia, the free encyclopedia

    To figure out the answer you will probably need to use the same techniques.

    Other than this I can only give you the hint that

    \sum _{j=1} ^n j^k is a polynomial of degree k+1, this means that you can find the closed formula by evaluating at k+2 points, and interpolating them (since there is a unique interpolating polynomial.)
    Last edited by gmatt; November 12th 2009 at 10:50 PM.
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