Use the limit comparison test to determine whether ?n=15??an?=?n=15??6+3n46n3?6n2+15? converges or diverges. (a) Choose a series ?n=16??bn? with terms of the form bn?=np1? and apply the limit comparison test. Write your answer as a fully simplified fraction. For n?15 limn???bn?an??=limn??? (b) Evaluate the limit in the previous part. Enter ? as in solutionspile.com

Question

Use the limit comparison test to determine whether

?_{n = 15}^{?} a_{n} = ?_{n = 15}^{?} \frac{6 n ^{3} ? 6 n ^{2} + 15}{6 + 3 n ^{4}}

converges or diverges. (a) Choose a series

?_{n = 16}^{?} 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 ? 15

lim_{n ? ?} \frac{a _{n}}{b _{n}} = lim_{n ? ?}

(b) Evaluate the limit in the previous part. Enter

?

as infinity and

? ?

as -infinity. If the limit does not exist, enter DNE.

lim_{n ? ?} \frac{a _{n}}{b _{n}} =

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

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