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    We all know \displaystyle\sum_{r=1}^n r^2 = \frac{1}{6}n(n+1)(2n+1).

    But what about this:

    \displaystyle\sum_{r=1}^n r^r = \mathrm{f}(n)

    ?

    I.e. 1 + 4 + 27 + 256 + 3125 + 46656 + ... + n^n ?
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    Wow... I have no idea how to find a formula for that... how about we try induction for every possible formula? :p:

    PS: What does the r^2 example have to do with the second one? :confused:
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    Just to show it is an example.
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    Just as not all integrals can be expressed with elementary functions, I think, this summation has no closed-form expression. But I'm not sure.
 
 
 

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