Suppose an and bnare series with positive terms and > bn is known to be convergent.(a) If an > bn for all n, what can you say about ) an? Why?an converges by the Comparison Test.an converges if and only if an < 2bn.an diverges by the Comparison Test.an converges if and only ifan< 4bn.We cannot say anything about) an.(b) If an < bn for all n, what can you say about > an? Why?an converges by the Comparison Test.2 an converges if and only ifDn.< an s bn.2bn.an converges if and only if .< an < bn.4O We cannot say anything about > an.> an diverges by the Comparison Test.

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Suppose an and bn are series with positive terms and > bn is known to be convergent. (a) If an > bn for all n, what can you say about ) an? Why? an converges by the Comparison Test. an converges if and only if a, < 2bn. an diverges by the Comparison Test. an converges if and only if an < 4bn. O We cannot say anything about > an. (b) If an < bn for all n, what can you say about ) an? Why? 2 an converges by the Comparison Test. 2an converges if and only if s an 2 O an converges if and only if n < an s bn. We cannot say anything about ) an. O) an diverges by the Comparison Test.

Suppose an and bn are series with positive terms and > bn is known to be convergent. (a) If an > bn for all n, what can you say about ) an? Why? an converges by the Comparison Test. an converges if and only if a, < 2bn. an diverges by the Comparison Test. an converges if and only if an < 4bn. O We cannot say anything about > an. (b) If an < bn for all n, what can you say about ) an? Why? 2 an converges by the Comparison Test. 2an converges if and only if s an 2 O an converges if and only if n < an s bn. We cannot say anything about ) an. O) an diverges by the Comparison Test.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.3: Geometric Sequences

Problem 44E

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Question

Suppose an and bn
are series with positive terms and > bn is known to be convergent.
(a) If an > bn for all n, what can you say about ) an? Why?
an converges by the Comparison Test.
an converges if and only if an < 2bn.
an diverges by the Comparison Test.
an converges if and only if
an
< 4bn.
We cannot say anything about) an.
(b) If an < bn for all n, what can you say about > an? Why?
an converges by the Comparison Test.
2 an converges if and only if
Dn.
< an s bn.
2
bn.
an converges if and only if .
< an < bn.
4
O We cannot say anything about > an.
> an diverges by the Comparison Test.

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