For each sequence a, find a number k such that n'an has a finite non-zero limit. (This is of use, because by the limit comparison test the series > an and >n-k both converge or both Σ Σ n=1 n=1 diverge.) А. ат — (4+ 2n)-2 k = 2 В. а, — nº +n k = 2n2+2n+2 С. ап 6n°+6n+2 k =

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 49E
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For each sequence a, find a number k such
that n'an
has a finite non-zero limit.
(This is of use, because by the limit comparison test
the series > an and >n-k both converge or both
Σ
Σ
n=1
n=1
diverge.)
А. ат —
(4+ 2n)-2
k =
2
В. а, —
nº +n
k =
2n2+2n+2
С. ап
6n°+6n+2
k =
Transcribed Image Text:For each sequence a, find a number k such that n'an has a finite non-zero limit. (This is of use, because by the limit comparison test the series > an and >n-k both converge or both Σ Σ n=1 n=1 diverge.) А. ат — (4+ 2n)-2 k = 2 В. а, — nº +n k = 2n2+2n+2 С. ап 6n°+6n+2 k =
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