The series that I'm working with is: (Series, n=1 -> infinity) n!/e^{n^2 }

I decided that the ratio test would be my best bet, so I have come to the limit_{(}_{n-> infinity)}(n+1)/(e^{2n+1}).

I know that this limit is infinity/infinity at the moment, which is indeterminate. Usually what I would do is place every term over the highest

n power, but I get confused with the e term in the denominator.

My book says that this limit = 0, which would make it convergent, I just get mixed up in the middle.

What is the right approach to figuring out this limit?

Thanks.