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Find the limit: $\lim_{n\to\infty} \left (1+ \frac {1}{2^2}+ \frac {1}{3^3}+...+\frac {1}{n^n} \right)$ [duplicate]
Does the limit:
$$\lim_{n\to\infty} \left (1+ \frac {1}{2^2}+ \frac {1}{3^3}+...+\frac {1}{n^n} \right)$$
admit a closed form?
I know only Riemann-Zeta function.I've just discovered this sum.
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Limit at Infinity $\lim\limits_{m\to\infty}\frac{\sum\limits_{k=1}^m\cot^{2n+1}\left(\frac{k\pi}{2m+1}\right)}{m^{2n+1}}$
How can I prove the following equality?
$$\lim_{m\to{\infty}}\frac{\displaystyle\sum_{k=1}^m\cot^{2n+1}\left(\frac{k\pi}{2m+1}\right)}{m^{2n+1}}=\frac{2^{2n+1}\zeta(2n+1)}{\pi^{2n+1}}$$
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