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Solution: Series to functions Find the function represented

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

Solution for problem 54E 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 54E

Series to functions Find the function represented by the following series and find the interval of convergence of the series.

\(\sum_{k=1}^{\infty} \frac{x^{2 k}}{4 k}\)

Step-by-Step Solution:

Solution 54EStep 1:In this problem we have to find the function represented by the seriesand also we have to find the interval of convergence of the series.We compute the derivative of this power series by differentiating term-by-term: (Since ) where we’ve computed the sum by summing a geometric series with common ratio , so that the last series converges whenever and diverges when . That means that the interval of convergence of the last series is (1, 1) with or without the endpoints.

Step 2 of 3

Chapter 9.2, Problem 54E is Solved
Step 3 of 3

Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

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Solution: Series to functions Find the function represented