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

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
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Chapter9: Sequences, Probability And Counting Theory
Section: Chapter Questions
Problem 23RE: Use the formula for the sum of the first ii terms of an arithmetic series to find the sum of the...
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Suppose Fa. and b, are series with positive terms and o, is known to be convergent.
b,
in
(a) If a, > b, for all n, what can you say about
? Why?
O We cannot say anything about a,
Sa, converges by the Comparison Test.
in
Sa, converges if and only if a, < 2b,.
Sa, converges if and only if a, < 4b,-
Sa, diverges by the Comparison Test.
(b) If a, < b, for all n, what can you say about Fa? Why?
in
an
b,
Oa, converges if and only if
<an s bn.
2
n°
O a, diverges by the Comparison Test.
bn
> a, converges if and only if
<an s bn.
4
We cannot say anything about a,
>'a, converges by the Comparison Test.
Transcribed Image Text:Suppose Fa. and b, are series with positive terms and o, is known to be convergent. b, in (a) If a, > b, for all n, what can you say about ? Why? O We cannot say anything about a, Sa, converges by the Comparison Test. in Sa, converges if and only if a, < 2b,. Sa, converges if and only if a, < 4b,- Sa, diverges by the Comparison Test. (b) If a, < b, for all n, what can you say about Fa? Why? in an b, Oa, converges if and only if <an s bn. 2 n° O a, diverges by the Comparison Test. bn > a, converges if and only if <an s bn. 4 We cannot say anything about a, >'a, converges by the Comparison Test.
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