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$$\sum^N\frac{1}{n^n} = 1 / 1^1 + 1/2^2 + 1/3^3 + 1/4^4 \ + \dotsb= 1.291285997... \text{ for }\ N \to \infty $$

Maybe this is related to the Riemann-Zeta function? I'm taking a wild guess.

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    $\begingroup$ Read about Sophomore's dream $\endgroup$
    – Bach
    Commented Feb 11, 2014 at 6:52
  • $\begingroup$ Woa. I just discovered an identity without even knowing it. +1. $\endgroup$ Commented Feb 11, 2014 at 6:56
  • $\begingroup$ It's a particular value of the Sophomore's dream function : $Sphd(-1,1)$ , from Eq.7:4 in "The Sophomore's dream function" : fr.scribd.com/doc/34977341/Sophomore-s-Dream-Function $\endgroup$
    – JJacquelin
    Commented Feb 11, 2014 at 9:13

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Hans Zauber pointed out that this is part of an identity called "sophomore's dream" that was discovered by Bernoulli.

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  • $\begingroup$ Well, to be precise, this is just the number involved in the identity. It's not an identity without both side of the equals sign. :) $\endgroup$
    – user856
    Commented Feb 11, 2014 at 8:37

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