(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the interval of convergence of: ##\sum\frac{n^n}{n!}z^n##

2. Relevant equations

3. The attempt at a solution

I obtained that the radius of convergence is ##1/e## but I am not sure what to do at the end points. For ##z=1/e## I would have ##\sum{n^n}{n!e^n}##.

Mod edit: I think you mean ##\sum \frac{n^n}{n!e^n}##.

Using Stirling formula I would obtain an approximation of the form ##\sum \frac{1}{\sqrt{2 \pi n}}##, which would go to infinity. However I am not sure how to make it formal, as this approximation is not a lower, but an upper bound for n!. And how should I proceed for -1/e? Thank you!

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# Interval of convergence

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