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Explain why a power series is tested for absolute

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

Solution for problem 4E Chapter 9.2

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 4E

Explain why a power series is tested for absolute convergence.

Step-by-Step Solution:

Solution 4EExplain why a power series is tested for absolute convergence.Step 1:A power series about x=a is of the formTo test for the convergence of the series we will use a modified ratio test.It is given by The result of this test will be an absolute value of the form We will now determine where this expression is less than one. R is called the radius of convergence, and is the interval of convergence. The power series converges absolutely for any x in that interval.Therefore a power series is tested for absolute convergence

Step 2 of 1

Chapter 9.2, Problem 4E is Solved
Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

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Explain why a power series is tested for absolute