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Quick Clarification

  1. Oct 3, 2005 #1
    Quite Curious

    [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]
     
    Last edited: Oct 3, 2005
  2. jcsd
  3. Oct 3, 2005 #2

    shmoe

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    Science Advisor
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