Possible Duplicate:
“Closed” form for $\sum \frac{1}{n^n}$
One of the problems on the tryout exam for my university's Putnam team was to prove the following:
$$\int_0^1x^xdx=\sum_{n=1}^\infty(-1)^{n+1}n^{-n}$$
I was elated when I saw this, because I knew I had seen a proof somewhere; unfortunately, I completely failed to remember the proof, and thus afterward wanted to look it up. I then ran into the other problem that I don't remember the name of the identity, if it has a standard one (I remember a Wikipedia page calling it something like the "marvelous identity" or the "miraculous identity").
Thus, I'm really looking for two things- the name of this identity, if there is a standard one, and a proof of it.
