Use the limit comparison test to determine whether ( sum_{n=5}^{infty} a_{n}=sum_{n=5}^{infty} frac{9 n^{3}-9 n^{2}+5}{6+4 n^{4}} ) converges or diverges.
(a) Choose a series ( sum_{n=5}^{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 geq 5 )
[
lim _{n
ightarrow infty} frac{a_{n}}{b_{n}}=lim _{n
ightarrow 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. ( lim _{n
ightarrow infty} frac{a_{n}}{b_{n}}= )
(c) By the limit comparison test, does the series converge, diverge, or is the test inconclusive? Choose
