can you solve $33,50,51?23-56$ Determine whether the sequence converges or diverges.

If it converges, find the limit$.$

$a_n=\frac{3+5n^2}{n+n^2}$

$a_n=\frac{3+5n^2}{1+n}$

$a_n=\frac{n^4}{n^3-2n}$

$a_n=2+(0\mathrm{.}86{)}^n$

$a_n=3^n{7}^{-n}$

$a_n=\frac{3\sqrt[\phantom{2}]{n}}{\sqrt[\phantom{2}]{n}+2}$

$a_n=e^{-\frac{1}{\sqrt[\phantom{2}]{n}}}$

$a_n=\frac{4^n}{1+9^n}$

$a_n=\sqrt[\phantom{2}]{\frac{1+4n^2}{1+n^2}}$

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

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

$a_n=e^{2\frac{n}{n+2}}$

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

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

$\{\frac{(2n-1)!}{(2n+1)!}\}$

$\{\frac{lnn}{ln2n}\}$

$\{sinn\}$

$a_n=\frac{ta{n}^{-1}n}{n}$

$\{n^2{e}^{-n}\}$

$a_n=ln(n+1)-lnn{a}_n=\frac{(lnn{)}^2}{n}$

$a_n=arctan(lnn)$