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Calculus / Calculus: Early Transcendentals 1 / Chapter 9.4 / Problem 50E

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

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Solved: Representing functions by power series Identify

Chapter 8, Problem 50E

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QUESTION:

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

\(\sum_{k=0}^{\infty}(-1)^{k} \frac{x^{k}}{3^{k}}\)

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QUESTION:

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

\(\sum_{k=0}^{\infty}(-1)^{k} \frac{x^{k}}{3^{k}}\)

ANSWER:

Solution 50E
Step 1:

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

So,
${S}_{k}=\sum\limits_{k=0}%5$

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