Originally Posted by

**Bacterius** Hello,

In chemistry class, instead of working hard on valence shells and bonds, I've been fiddling with my calculator. I tried to evaluate the following sum out of interest :

$\displaystyle \sum_{k = 1}^{\infty} \frac{1}{k^k} \approx 1.291285 \cdots$

It converges. Has anyone ever seen this actual sum somewhere ? Does it have a particular meaning or use, as $\displaystyle \zeta{(s)}$ ? Or is it just yet another random and useless summation ? I'm asking the question because I feel this sum has something special, having the variable both in base and exponent.

I've been looking on Google but didn't find any reading on it. Any input is appreciated :)