Is there a general formula for
$$ \sum_{k=1}^{N} k^n $$
for integers $n \geq 1$? Wolfram alpha linked me the harmonic number but it doesn't seem to expand beyond negative values since $\Gamma(-n)=\widetilde{\infty}$
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1https://en.wikipedia.org/wiki/Faulhaber%27s_formula – Bart Michels Mar 04 '17 at 15:52
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1Possible duplicate of How is Faulhaber's formula derived? or if you are not interested in that, then possible duplicate of Methods to compute $\sum_{k=1}^nk^p$ without Faulhaber's formula – Simply Beautiful Art Mar 04 '17 at 15:52
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For $n=1,2,3$ we have general formulae. https://brilliant.org/wiki/sum-of-n-n2-or-n3/ – rookie Mar 04 '17 at 15:52
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Thank you!! Sorry, did not know the name. – Baklava Gain Mar 04 '17 at 15:56
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No problemo! =D – Simply Beautiful Art Mar 04 '17 at 15:57