Is there any formula to compute $\sum_{k=1}^n\frac {1}{k^k}$?

Asked Aug 23 '16 at 13:01

Active Aug 23 '16 at 13:05

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Is there any formula to compute $\sum_{k=1}^n\frac {1}{k^k}$? Where the value of $k$ ranges from $1$ to $n$.

edited Aug 23 '16 at 13:05

Winther

asked Aug 23 '16 at 13:01

ankit

1

There is no simple closed form for this sum. However you can write it as the integral $\int_0^1\frac{{\rm d}x}{x^x}$ if you want (when $k$ ranges from $1$ to $\infty$). – Winther Aug 23 '16 at 13:03
9

https://en.wikipedia.org/wiki/Sophomore's_dream – Watson Aug 23 '16 at 13:03

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