Determining if a sequence converges or diverges... Determine if the sequence $(a_n)$ defined by $a_n := \frac{\cos{\left(e^{n^n}\right)}}{n^2}$ converges or diverges. If it converges, determine its limit.
Okay so the solution is $0$ (so it does converge). I just have a question on where to start, clearly we cannot use L'Hopital's rule. Thank you for the help!

$0\leq |a_n| \leq \frac 1 {n^{2}}$. Use Squeeze Lemma. 
