Yet another convergence problem

[lmannoia]

Homework Statement

It's the sum (n=1 to infinity) of (n!)/(2^(n^2)) I hope that's not too hard to read?

Homework Equations

The ratio test, I think? Since it contains a factorial.

The Attempt at a Solution

It seems like I'm never short of calculus questions. Everytime I try to apply the ratio test, I end up getting to (n+1)(2^(n^2)) / (2^(n+1)^2) and I'm unsure of where to go from there to see if it converges or not.

 

[Bohrok]

Try expanding 2^(n+1)^2 and then rewrite that using some rules of exponents.