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

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

Algebra & Trigonometry with Analytic Geometry
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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Suppose a, andbn are series with positive terms and b. is known to be divergent. (a) If a, > b, for all n, what can you say about a.? Why? a, converges if and only if n-a, 2 b,. z bn a, converges if and only if 2a, a converges by the Comparison Test. We cannot say anything about a, Sa, diverges by the Comparison Test. (b) If a, < b, for all n, what can you say abouta? Why? O a, converges if and only if a, s 4 b, n a, converges if and only if a, n We cannot say anything about a, a, diverges by the Comparison Test. > a, converges by the Comparison Test. O O O
Transcribed Image Text:Suppose a, andbn are series with positive terms and b. is known to be divergent. (a) If a, > b, for all n, what can you say about a.? Why? a, converges if and only if n-a, 2 b,. z bn a, converges if and only if 2a, a converges by the Comparison Test. We cannot say anything about a, Sa, diverges by the Comparison Test. (b) If a, < b, for all n, what can you say abouta? Why? O a, converges if and only if a, s 4 b, n a, converges if and only if a, n We cannot say anything about a, a, diverges by the Comparison Test. > a, converges by the Comparison Test. O O O
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