If $n(n+1)(2n+1)/6 = 1^2 + 2^2 + \cdots + n^2$, then is there a formula to calculate $1^x + 2^x + \cdots + n^x$ where $x$ is a even number?
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6https://en.wikipedia.org/wiki/Faulhaber%27s_formula That wikipedia page also inludes the proof. – Harto Saarinen Nov 24 '15 at 16:24
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Faulhaber's formula is for positive even numbers. For also negative even numbers consider Euler summation formula, for the partial sums of $\zeta(x)$. – Dietrich Burde Nov 24 '15 at 16:28
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If $x$ is the even number 0 then the answer is $n$. – jbuddenh Nov 24 '15 at 16:38