Let $a_n=\frac{n^2}{n^4-3}$ and $b_n=\frac{1}{n^2}.$

Calculate the following limit$.$

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

$($Give an exact answer. Use symbolic notation and fractions where needed. Enter DNE if the limit does not exist.$)$

$\underset{x}{lim}\frac{a_{a_k}}{b_k}=$

$$

Devermise the coevergence of ${\displaystyle \underset{i=1}{\overset{}{}}}{a}_a.$

${\displaystyle \underset{=1}{\overset{\frac{?}{\text{b}\text{a}\text{r}}()}{}}}{a}_{}$ diverges by the Limit Comparison Test because ${\displaystyle \underset{=1}{\overset{\frac{?}{\text{b}\text{a}\text{r}}()}{}}}{}_{}$ diverges and $\underset{}{lim}={}_{}$ is infinite.

${\displaystyle \underset{n=1}{\overset{E}{}}}{a}_n$ comerges by the Limit Comparison Tembecaue ${\displaystyle \underset{n=1}{\overset{E}{}}}{A}_n$ converges and $\underset{a_4}{lim}$ exists and is finite.