1
$\begingroup$

This question already has an answer here:

I would like to ask if anyone would help me with solving the following infinite series. \begin{equation} \sum_{n=1}^{\infty} \frac{1}{n^n} = \,? \end{equation} Thank you in advance.

$\endgroup$

marked as duplicate by Hans Lundmark, metamorphy, Xander Henderson, Daryl, José Carlos Santos sequences-and-series Jun 7 at 22:12

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

6
$\begingroup$

Although it has no closed form, it does satisfy the remarkable identity $$ \sum_{n=1}^\infty \frac{1}{n^n} = \int_0^1\frac{dx}{x^x}. $$ It is also equal to $\ln(3)^e$ to five decimal places.

$\endgroup$

Not the answer you're looking for? Browse other questions tagged or ask your own question.