Exercises 47 and 48 complete the limit comparison test. 47. Let £ak and bk be series with positive terms. Suppose that ak/bk → 0. (a) Show that if bk converges, then ak converges. (b) Show that if ak diverges, then bx diverges. (c) Show by example that if ak converges, then E bx may converge or diverge. (d) Show by example that if bx diverges, then ak may converge or diverge. [Parts (c) and (d) explain why we stipulated L > 0 in Theo-
Exercises 47 and 48 complete the limit comparison test. 47. Let £ak and bk be series with positive terms. Suppose that ak/bk → 0. (a) Show that if bk converges, then ak converges. (b) Show that if ak diverges, then bx diverges. (c) Show by example that if ak converges, then E bx may converge or diverge. (d) Show by example that if bx diverges, then ak may converge or diverge. [Parts (c) and (d) explain why we stipulated L > 0 in Theo-
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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![Exercises 47 and 48 complete the limit comparison test.
47. Let Eaz and Ebk be series with positive terms. Suppose
that ak/bk → 0.
(a) Show that if bk converges, then ak converges.
(b) Show that if Ear diverges, then E bx diverges.
(c) Show by example that if ak converges, then bk may
converge or diverge.
(d) Show by example that if bk diverges, then ak may
converge or diverge.
[Parts (c) and (d) explain why we stipulated L > 0 in Theo-
rem 12.3.7.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb2108e9e-3d70-4ea0-8109-4b107d5ac154%2F46938244-d327-42f4-a3d3-d0a981a1807d%2Fqnx9kna_processed.png&w=3840&q=75)
Transcribed Image Text:Exercises 47 and 48 complete the limit comparison test.
47. Let Eaz and Ebk be series with positive terms. Suppose
that ak/bk → 0.
(a) Show that if bk converges, then ak converges.
(b) Show that if Ear diverges, then E bx diverges.
(c) Show by example that if ak converges, then bk may
converge or diverge.
(d) Show by example that if bk diverges, then ak may
converge or diverge.
[Parts (c) and (d) explain why we stipulated L > 0 in Theo-
rem 12.3.7.]
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