(1 point) Use the limit comparison test to determine whether \(\sum_{n=17}^{\infty} a_n = \sum_{n=17}^{\infty} \frac{7n^3 - 3n^2 + 17}{9 + 3n^4}\) converges or diverges.
(a) Choose a series \(\sum_{n=17}^{\infty} b_n\) 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 \(n \ge 17,\)
\(\lim_{n \to \infty} \frac{a_n}{b_n} = \lim_{n \to \infty} \frac{\text{____}}{\text{____}}\)
(b) Evaluate the limit in the previous part. Enter \(\infty\) as infinity and \(-\infty\) as -infinity. If the limit does not exist, enter DNE.
\(\lim_{n \to \infty} \frac{a_n}{b_n} = \text{____}\)
(c) By the limit comparison test, does the series converge, diverge, or is the test inconclusive? Choose
