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

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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 > an? Why?
O We cannot say anything about
2an converges if and only if 2a, 2 bn.
an converges if and only if n.an > bn:
an diverges by the Comparison Test.
Lan converges by the Comparison Test.
(b) If an < bn for all n, what can you say about > an? Why?
> an converges if and only if an <
> an converges if and only if an
bn.
2 an converges by the Comparison Test.
> an diverges by the Comparison Test.
O We cannot say anything about > an
ооо
Transcribed Image Text: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 > an? Why? O We cannot say anything about 2an converges if and only if 2a, 2 bn. an converges if and only if n.an > bn: an diverges by the Comparison Test. Lan converges by the Comparison Test. (b) If an < bn for all n, what can you say about > an? Why? > an converges if and only if an < > an converges if and only if an bn. 2 an converges by the Comparison Test. > an diverges by the Comparison Test. O We cannot say anything about > an ооо
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