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Combining power series Use the power series representation

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

Solution for problem 28E 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 28E

Combining power series Use the power series representation

to find the power series for the following functions (centered at 0). Give the interval of convergence of the new series.

g(x) = x3 ln(l − x)

Step-by-Step Solution:

Solution 28EStep 1:

Given Using the power series representation for , we get

Step 2:

Series isand

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     For the series to be convergent .

So, the radius of convergence is 1.

Step 3 of 3

Chapter 9.2, Problem 28E is Solved
Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

The answer to “Combining power series Use the power series representation to find the power series for the following functions (centered at 0). Give the interval of convergence of the new series.g(x) = x3 ln(l ? x)” is broken down into a number of easy to follow steps, and 34 words. Since the solution to 28E from 9.2 chapter was answered, more than 247 students have viewed the full step-by-step answer. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. This full solution covers the following key subjects: Series, power, interval, Find, functions. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. The full step-by-step solution to problem: 28E from chapter: 9.2 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1.

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