sequences and series - What is exact value of $sum_{n=1}^{infty} frac{1}{n^n}$ .

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.

Answer

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.