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52-57. Choose your test Determine whether the following series con- verge or diverge. 52. 8 54. Σ k=0 k + 1 k 10 k² + 9 53. Ο 1 k= (3k + 1)(3k + 4) k ένα k=0 k² + 1 55. Σ α

52-57. Choose your test Determine whether the following series con- verge or diverge. 52. 8 54. Σ k=0 k + 1 k 10 k² + 9 53. Ο 1 k= (3k + 1)(3k + 4) k ένα k=0 k² + 1 55. Σ α

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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help with 55, explain how to do divergence test then perform otehr test to determine the convergence and divergence of this series?

or why not Determine whether the following state- ments are true and give an explanation or counterexample. a. If Σa, converges, then Σ ak converges. k= k=10 b. If Σakdiverges, then Σ ak diverges. k=1 k=10 c. If a converges, then Σ(ak + 0.0001) also converges. d. If Ep diverges, then Σ(p + 0.001)* diverges, for a fixed real number p. If Ek converges, then Σk-P+0.001 converges. e. f. If lim ak = 0, then Zak converges. kis 52-57. Choose your test Determine whether the following series con- verge or diverge. 52. Σ 54. IM8 IM 56. Σ k + 1 k 10 k² +9 2k + 3k 4k 53. 55. 57. 58. Log p-series Consider the series number. 12 1 Σ Σ k=1 (3k + 1)(3k + 4) 8 Σ k=0 or k √₁² + 1 1 k=2 k(ln k)p' 59. Loglog p-series Consider the series is a real number. ∞4 Σ {₂k1 k=2 k ln² k a. Use the Integral Test to determine the values of p for which this series converges. b. Does this series converge faster for p = 2 or p = 3? Explain. where p is a real 1 k=3 k ln k(In ln k)p³ a. For what values of p does this series converge? b. Which of the following series converges faster? Explain. 1 where p 1 Σ 2k In k(In Ink)² 65. 66
Transcribed Image Text:or why not Determine whether the following state- ments are true and give an explanation or counterexample. a. If Σa, converges, then Σ ak converges. k= k=10 b. If Σakdiverges, then Σ ak diverges. k=1 k=10 c. If a converges, then Σ(ak + 0.0001) also converges. d. If Ep diverges, then Σ(p + 0.001)* diverges, for a fixed real number p. If Ek converges, then Σk-P+0.001 converges. e. f. If lim ak = 0, then Zak converges. kis 52-57. Choose your test Determine whether the following series con- verge or diverge. 52. Σ 54. IM8 IM 56. Σ k + 1 k 10 k² +9 2k + 3k 4k 53. 55. 57. 58. Log p-series Consider the series number. 12 1 Σ Σ k=1 (3k + 1)(3k + 4) 8 Σ k=0 or k √₁² + 1 1 k=2 k(ln k)p' 59. Loglog p-series Consider the series is a real number. ∞4 Σ {₂k1 k=2 k ln² k a. Use the Integral Test to determine the values of p for which this series converges. b. Does this series converge faster for p = 2 or p = 3? Explain. where p is a real 1 k=3 k ln k(In ln k)p³ a. For what values of p does this series converge? b. Which of the following series converges faster? Explain. 1 where p 1 Σ 2k In k(In Ink)² 65. 66
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