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+00 +00 (a) Suppose that 2 an and 2 b, are series with positive terms n=1 n=1 +oo an and that > b, is convergent. Prove that if lim n→+∞ b, %3D n=1 +0o then a, is also convergent. n=1

+00 +00 (a) Suppose that 2 an and 2 b, are series with positive terms n=1 n=1 +oo an and that > b, is convergent. Prove that if lim n→+∞ b, %3D n=1 +0o then a, is also convergent. n=1

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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This is a two-part problem regarding comparison tests for infinite series. 

+oo +oo - (a) Suppose that > an and 2 b, are series with positive terms n=1 n=1 and that > b, is convergent. Prove that if lim n→+∞ b. n n=1 then a, is also convergent. n=1 (b) Use part (a) to show that the series converges. +o0 In (n) (1) E In (n) (ii) E n=1 Vn · en n3 n=1 ||
Transcribed Image Text:+oo +oo - (a) Suppose that > an and 2 b, are series with positive terms n=1 n=1 and that > b, is convergent. Prove that if lim n→+∞ b. n n=1 then a, is also convergent. n=1 (b) Use part (a) to show that the series converges. +o0 In (n) (1) E In (n) (ii) E n=1 Vn · en n3 n=1 ||
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