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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- Nov 10th 2009, 03:46 PMhwcorleySum 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] ?

- Nov 12th 2009, 08:00 PMgmatt
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

$\displaystyle \sum _{j=1} ^n j^k$ 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.)