Evaluating $\sum_{n=0}^\infty \frac{1}{n^n}$

Asked Jul 27 '19 at 05:46

Active Jul 27 '19 at 06:34

Viewed 43 times

$$\sum_{n=0}^\infty \frac{1}{n^n}$$

it's easy to see that this series converge by using ratio test, but i have no idea what this series converges to

there might be some problem with $0^0$ if that's the case, i would like to change the lowest bound to $n=1$ or $\displaystyle\sum_{n=1}^\infty \frac{1}{n^n}$

i'm just curious on how to tackle this kind of problem

edited Jul 27 '19 at 06:34

StubbornAtom

17,052

asked Jul 27 '19 at 05:46

Running Ray

The other two times this was asked no answers came. I guess the only things worth knowing about this series are that it converges by almost any test and that we have the result known as Sophomore's dream. – Jyrki Lahtonen Jul 27 '19 at 06:03
1

@JyrkiLahtonen Done! – Robert Z Jul 27 '19 at 06:09

Evaluating $\sum_{n=0}^\infty \frac{1}{n^n}$

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