Use the $limit$ comparison test $to$ determine whether ${\displaystyle \underset{n=5}{\overset{}{}}}{a}_n={\displaystyle \underset{n=5}{\overset{}{}}}\frac{7n+4}{5n^6+2n^2+8}$

converges $or$ diverges.

$a.$ Choose a series ${\displaystyle \underset{n=5}{\overset{}{}}}{b}_n$ with terms $of$ the form $b_n=\frac{1}{n^p}$ and apply the $limit$

comparison test. Choose the largest $p$ that works. Write your answer $as$ a fully

simplified fraction.

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

$b.$ Evaluate the $limitin$ the previous part. Give $an$ exact answer $if$ the $limitis$ a number.

Otherwise, enter $-orif$ the $limitis$ infinite, $or$ enter DNE $if$ the $limit$ does not

exist $in$ another way.

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

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

inconclusive?