$a_n=\frac{(-3{)}^{2n}}{1+3n^3+9^{n+1}}$

$a_n=\frac{\sqrt[\phantom{2}]{9+n^2+4n^4}}{(n+3n^{\frac{3}{2}})(4+\sqrt[\phantom{2}]{n})}$

$a_n=\sqrt[\phantom{2}]{\frac{n+1}{9n+1}}$

$a_n=\frac{(1{)}^{n+1}n}{(\sqrt[\phantom{2}]{n}+100{)}^2}$

$a_n=\frac{ln(n)}{ln(2n)}$

$q_n=\frac{n}{n+1}cos(n)$

$q_n=n-\sqrt[\phantom{2}]{n^2-n}$

$a_n=\frac{2^n+5^{n+2}}{6^n}$

Find the limit of the sequence $\{a_n\}$ or prove that the limit DNE