Using the Divergence Test and l'Hopital's Rule (and the rule that lets me take the exponent outside the limit), I got that the series diverged:
http://goo.gl/KVYEKZ
Edited to add:
Graph of the series (to confirm my working):
After thinking about this problem a bit more, I was wondering if this logic would work: as x→∞, the sum will resemble Σ1^(2x), which is just Σ1^(x), which diverges by the Geometric Series test (since it's just 1+1+1+1 infinite times). I get the same result, but I feel like I'm messing up something by applying l'Hopital's rule like that...