Question

find the limit of the sequence a_n = (1/(e^(4n)+n^2)^(1/n)?

Answer 1

sequence goes to infinity

Answer 2

\[\lim_{n\to \infty}\frac{1}{\left(e^{4n}+n^2\right)^{\frac{1}{n}}}\]?

Answer 3

yeah

Answer 4

i think the best bet is to rewrite as
\[\left(e^{4n}+n^2\right)^{-\frac{1}{n}}\] then take the log to get
\[-\frac{1}{n}\ln(e^{4n}+n^2)\] and use l'hopital

Answer 5

is -ln(e^(4n)+n^2) the same as ln(e^(4n)+n^2)^-1?