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Exercise 2.7.4. Give an example of each or explain why the request is impos- sible referencing the proper theorem(s). (a) Two series xn and Σyn that both diverge but where nyn converges. (b) A convergent series xn and a bounded sequence (yn) such that Σnyn diverges. (c) Two sequences (xn) and (yn) where Σn and Σ(n+yn) both converge but yn diverges. (d) A sequence (xn) satisfying 0 < x < 1/n where Σ(-1)xn diverges. the basic facts about geometric

Exercise 2.7.4. Give an example of each or explain why the request is impos- sible referencing the proper theorem(s). (a) Two series xn and Σyn that both diverge but where nyn converges. (b) A convergent series xn and a bounded sequence (yn) such that Σnyn diverges. (c) Two sequences (xn) and (yn) where Σn and Σ(n+yn) both converge but yn diverges. (d) A sequence (xn) satisfying 0 < x < 1/n where Σ(-1)xn diverges. the basic facts about geometric

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 82E
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Exercise 2.7.4. Give an example of each or explain why the request is impos- sible referencing the proper theorem(s). (a) Two series xn and Σyn that both diverge but where nyn converges. (b) A convergent series xn and a bounded sequence (yn) such that Σnyn diverges. (c) Two sequences (xn) and (yn) where Σn and Σ(n+yn) both converge but yn diverges. (d) A sequence (xn) satisfying 0 < x < 1/n where Σ(-1)xn diverges. the basic facts about geometric
Transcribed Image Text:Exercise 2.7.4. Give an example of each or explain why the request is impos- sible referencing the proper theorem(s). (a) Two series xn and Σyn that both diverge but where nyn converges. (b) A convergent series xn and a bounded sequence (yn) such that Σnyn diverges. (c) Two sequences (xn) and (yn) where Σn and Σ(n+yn) both converge but yn diverges. (d) A sequence (xn) satisfying 0 < x < 1/n where Σ(-1)xn diverges. the basic facts about geometric
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