Ok. Calculus Question. Limit of infinite sequence, a_n.?

Question

Ok, so this is very stupid. Please tell me how to do it.

Lim as n->infinity of a_n= ( 1/ ( e^(4n) +n^2) )^ (1/n)

Apparently the answer is not 0, 1/e, or 1. Go figure.

Answer 1

[n→∞]lim ( 1/ ( e^(4n) +n^2) )^(1/n)
[n→∞]lim 1/ ( e^(4n) +n^2)^(1/n)
1/[n→∞]lim (e^(4n) +n^2)^(1/n)
1/[n→∞]lim (e^(4n))^(1/n) (n² term is negligible next to e^(4n)
1/[n→∞]lim e^4
1/e^4
e^(-4)

Answer 2

no solution after about 50 you get error on your calculator