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Power series from the geometric series Use the geometric I

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

Solution for problem 21RE 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 21RE

Power series from the geometric series Use the geometric series \(\sum_{k=0}^{\infty} x^{k}=\frac{1}{1-x}\), for |x| < 1 to determine the Maclaurin series and the interval of convergence for the following functions.

\(f(x)=\frac{1}{1-x^{2}}\)

Step-by-Step Solution:

Solution 21RE

Step 1:

In this problem we have to use the geometric series for |x|<1, to determine the Maclaurin series of and also we have to find the interval of convergence.

We have

Using geometric series  for |x| < 1 we get,

Thus the Maclaurin series of is given by

Notice that we replaced both the x in the geometric series with to get the required Maclaurin series and so we will do the same in the interval of convergence.

 

Thus  provided

Thus the interval of convergence for the Maclaurin series is . That is  the interval of convergence is

       

Step 2 of 1

Chapter 9, Problem 21RE is Solved
Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

The answer to “?Power series from the geometric series Use the geometric series \(\sum_{k=0}^{\infty} x^{k}=\frac{1}{1-x}\), for |x| < 1 to determine the Maclaurin series and the interval of convergence for the following functions.\(f(x)=\frac{1}{1-x^{2}}\)” is broken down into a number of easy to follow steps, and 30 words. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. Since the solution to 21RE from 9 chapter was answered, more than 283 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, geometric, interval, Convergence, functions. This expansive textbook survival guide covers 112 chapters, and 7700 solutions. The full step-by-step solution to problem: 21RE from chapter: 9 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM.

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Power series from the geometric series Use the geometric I