Use the $limit$ comparison test $to$ determine whether ${\displaystyle \underset{n=12}{\overset{}{}}}{a}_n={\displaystyle \underset{n=12}{\overset{}{}}}\frac{2n^3-8n^2+12}{3+7n^4}$

converges $or$ diverges.

$(a)$ Choose a series ${\displaystyle \underset{n=12}{\overset{}{}}}{b}_n$ with terms $of$ the form $b_n=\frac{1}{n^p}$ and apply the $limit$ comparison

test. Write your answer $as$ a fully simplified fraction. For $n12,$

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

$(b)$ Evaluate the $limitin$ the previous part. Enter $as$ infinity and $-as-$infinity. $If$ the

$limit$ does not exist, enter DNE.

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

$(c)By$ the $limit$ comparison test, does the series converge, diverge, $oris$ the test

inconclusive?