8m3 -61m2 8 converges or diverges 6 3m4 (1 pt) Use the limit comparison test to

Question

8m3 -61m2 8 converges or diverges 6 3m4 (1 pt) Use the limit comparison test to determine whether an n-8. n-8. (a) Choose a series bn with terms of the form b and apply the limit comparison test. Write your answer as a fully simplified n-8, fraction. For n 8, lim lim n (b) Evaluate the limit in the previous part. Enter as infinity and -oo as -infinity If the limit does not exist, enter DNE. lim n OO (C) By the limit comparison test, does the series converge, diverge, or is the test inconclusive? Choose

Explanation / Answer

a)

an =(8n^3 -6n^2 +8)/(6 +3n^4)

bn =(8n^3)/(3n^4) =8/(3n)

b)lim n->infinity [(8n^3 -6n^2 +8)/(6 +3n^4)]/[8/3n]

=lim n->infinity [(24n^4 -18n^3 +24n)/(48 +24n^4)]

=lim n->infinity [(24 -18/n + 24/n^3)/(48/n^4 +24)]

=[(24 -0 + 0)/(0 +24)]

=1

c) bn=8/3n diverges so "an" also diverges by limit comparision test

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