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Radius and interval of convergence Use the Ratio or Root

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett ISBN: 9780321570567 2

Solution for problem 15RE Chapter 9

Calculus: Early Transcendentals | 1st Edition

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Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

Calculus: Early Transcendentals | 1st Edition

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Problem 15RE

Radius and interval of convergence Use the Ratio or Root Test to determine the radius of convergence of the following power series. Test the endpoints to determine the interval of convergence, when appropriate.

Step-by-Step Solution:

Solution 15REStep 1:Given series is and To determine the radius of convergence we use ratio test which states:The ratio test states that:a. If then the series convergesb. If then the series divergesc. If or the limit does not exist then the test is inconclusive.Calculating L, we get Since and independent of x, we can conclude that the series converges for all x.Thus the interval of convergence is the interval . The radius of convergence in this case is said to be .

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Chapter 9, Problem 15RE is Solved
Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

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Radius and interval of convergence Use the Ratio or Root