Series 1^k+2^k+...+n^k.

I have found here: Power Series the formulas for 1<k<11. Could someone provide the formulas for 10<k<20 or more?

Thanks.

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- October 29th 2006, 12:11 PMtaras[SOLVED] Sum of power series
Series 1^k+2^k+...+n^k.

I have found here: Power Series the formulas for 1<k<11. Could someone provide the formulas for 10<k<20 or more?

Thanks. - October 29th 2006, 12:21 PMCaptainBlack
You will find the sum for arbitary power k in terms of the Bernoulli polynomials and Bernoulli numbers here.

RonL - October 29th 2006, 02:31 PMThePerfectHacker
Some theory heir