a$)$ LeT $a_n=\frac{n^2}{n^4-2}$ and $b_n=\frac{1}{n^2}$

calculate the following limit

$\underset{n}{lim}\frac{a_n}{b_n}=$

b$)$ Deternine the convergence of ${\displaystyle \underset{n=1}{\overset{}{}}}{a}_n$

${\displaystyle \underset{n=1}{\overset{}{}}}{a}_n$ direrges by the limit comparison test becouse ${\displaystyle \underset{n=1}{\overset{}{}}}{b}_n$ divarges $\underset{n}{lim}\frac{a_n}{b_n}$ converges

converses diverges