Representing functions by power series Identify the

Problem 49E Chapter 9.4

Calculus: Early Transcendentals | 1st Edition

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Problem 49E

Representing functions by power series Identify the functions represented by the following power series.

Step-by-Step Solution:

Solution 49EStep 1:

$\sum\limits_{k=0}^{\infty{}}\frac{{x}^{k}}{{2}^{k}}=1+\frac{1}{2}x+\frac{1}{{2}^{2}}{x}^{2}+\frac{1}{{2}^{3}}{x}^{3}+.......$ is an infinite geometric series where $a=1$ and $r=\frac{1}{2}x$ .

So, ${S}_{k}=\sum\limits_{k=0}^{\infty{}}\frac{{x}^{k}}{{2}^{k}}=1+\frac{1}{2}x+\frac{1}{{2}^{2}}{x}^{2}+\frac{1}{{2}^{3}}{x}^{3}+.......$

As we know that sum of an infinite geometric series is ${S}_{n}=\frac{a}{1-r}$ where...

Step 2 of 3

Chapter 9.4, Problem 49E 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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