$$\sum^N\frac{1}{n^n} = 1 / 1^1 + 1/2^2 + 1/3^3 + 1/4^4 \ + \dotsb= 1.291285997... \text{ for }\ N \to \infty $$
Maybe this is related to the Riemann-Zeta function? I'm taking a wild guess.
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2Read about Sophomore's dream – Bach Feb 11 '14 at 06:52
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Woa. I just discovered an identity without even knowing it. +1. – Armend Veseli Feb 11 '14 at 06:56
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It's a particular value of the Sophomore's dream function : $Sphd(-1,1)$ , from Eq.7:4 in "The Sophomore's dream function" : http://fr.scribd.com/doc/34977341/Sophomore-s-Dream-Function – JJacquelin Feb 11 '14 at 09:13
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Hans Zauber pointed out that this is part of an identity called "sophomore's dream" that was discovered by Bernoulli.
Armend Veseli
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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. :) – Feb 11 '14 at 08:37