TITLE: Is there any closed form for $\sum_{k=1}^n \frac{1}{k^k}$?
QUESTION [5 upvotes]: Is there any closed form for the summation:
$$\sum_{k=1}^n \frac{1}{k^k} = ? $$
or at least a tight lower bound?

REPLY [8 votes]: J. Bernoulli showed that 
$$\sum_{n=1}^\infty n^{-n}= \int_0^1 x^{-x}\,dx$$
This result is often called the "Sophomore's dream" because it looks too good to be true.
I don't believe there is a form more "closed" than this.