Use the limit comparison test to determine whether $\displaystyle \sum_{n=2}^{\infty} a_n = \sum_{n=2}^{\infty} \frac{9 n + 6}{2 n^{5} + 2n^2 + 7}$ converges or diverges.

(a) Choose a series $\displaystyle \sum_{n=2}^\infty b_n$ with terms of the form $\displaystyle b_n = \frac{1}{n^p}$ and apply the limit comparison test. Write your answer as a fully reduced fraction. For $n \geq 2$,

$\displaystyle \lim_{n \to \infty} \frac{ a_{n} }{ b_{n} } = \lim_{n \to \infty}$

(b) Evaluate the limit in the previous part. Enter $\infty$ as infinity and $-\infty$ as -infinity. If the limit does not exist, enter DNE.
$\displaystyle \lim_{n\to\infty} \frac{a_{n}}{b_{n}} \,$ =

(c) By the limit comparison test, does the series converge, diverge, or is the test inconclusive? Choose Converges Diverges Inconclusive