The original series is the sum from n=1 to infinity of (n!*x^n)/(n^n)(adsbygoogle = window.adsbygoogle || []).push({});

I used a ratio test to find that the interval of convergence is -e < x < e

But now I need to test the endpoints, which means I need to find if the following two series converge:

sum from n=1 to infinity of (n!*e^n)/(n^n)

sum from n=1 to infinity of (n!*(-e)^n)/(n^n)

I started with the first one, because the second is just an alternating version of it (right?) so if I proved absolute convergence I wouldn't have to do the second one as well. Here is where I am having problems though, I can't figure out a test that would prove divergence or convergence for the first one. I tried a ratio test, but I get an answer of 1 (inconclusive), which makes sense since I used a ratio to find the interval of convergence. Can someone point me in the right direction?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Interval of convergence problem

**Physics Forums | Science Articles, Homework Help, Discussion**