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.
1 Answer
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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.
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$\begingroup$ Thank you very much. $\endgroup$– user675788Jun 11, 2019 at 9:50