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

given an and bn are series series with positive terms

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

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

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section: Chapter Questions

Problem 63RE

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Question

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

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