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[tex] \begin{gathered}

\sum\limits_{i = 1}^n i = \frac{{n\left( {n + 1} \right)}}

{2} \hfill \\

\sum\limits_{i = 1}^n {i^2 } = \frac{{n\left( {n + 1} \right)\left( {2n + 1} \right)}}

{6} \hfill \\

\sum\limits_{i = 1}^n {i^3 } = \frac{{n^2 \left( {n + 1} \right)^2 }}

{4} \hfill \\

\vdots \hfill \\

\left( {etc} \right) \hfill \\

\end{gathered} [/tex]

------------------------------------------------

But in general,

[tex] \forall k \in \mathbb{N} , [/tex]

what is the general summation formula for

[tex] \sum\limits_{i = 1}^n {i^k } \; {?} [/tex]

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# Quick Clarification

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