- #1
Silviu
- 624
- 11
Homework Statement
Find the interval of convergence of: ##\sum\frac{n^n}{n!}z^n##
Homework Equations
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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