The original series is the sum from n=1 to infinity of (n!*x^n)/(n^n) 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?