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Let E-1 an and En=1 bn be convergent series of positive terms. (a) Why is it true that an < 1 for large values of n? (b) Using part (a), show that anbn < bn for large values of n. (c) Show that En=1anbn converges. (d) Using part (c), show that En=1 an converges. 2%3D1

Let E-1 an and En=1 bn be convergent series of positive terms. (a) Why is it true that an < 1 for large values of n? (b) Using part (a), show that anbn < bn for large values of n. (c) Show that En=1anbn converges. (d) Using part (c), show that En=1 an converges. 2%3D1

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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Let E-1 an and En-1 bn be convergent series of positive terms. (a) Why is it true that an < 1 for large values of n? (b) Using part (a), show that anbn < bn for large values of n. (c) Show that En=1anbn converges. (d) Using part (c), show that E=1 an converges.
Transcribed Image Text:Let E-1 an and En-1 bn be convergent series of positive terms. (a) Why is it true that an < 1 for large values of n? (b) Using part (a), show that anbn < bn for large values of n. (c) Show that En=1anbn converges. (d) Using part (c), show that E=1 an converges.
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