I wanted to know if there is a formula for ∑nk=1kx∑k=1nkx?
For example, for $x = 1$ we have : $N (N + 1) / 2$.
Also, for $x = 2$ we have : $N ( N + 1 ) ( 2n + 1 ) / 6$.
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You are looking for Faulhaber's formula https://en.wikipedia.org/wiki/Faulhaber%27s_formula – TomGrubb Sep 13 '17 at 00:30
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Well I know that: $$\sum_{k = 1}^{n}k^3 = \bigg(\sum_{k = 1}^{n}k\bigg)^2$$ That is a formula for $x = 3$. I am not aware of a general formula concerning any value for $x$ – Mr Pie Sep 13 '17 at 02:52
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Possible duplicate of How is Faulhaber's formula derived? – Hans Lundmark Sep 13 '17 at 05:52