Representing functions by power series Identify the

Chapter 8, Problem 49E

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QUESTION:

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

\(\sum_{k=0}^{\infty} \frac{x^{k}}{2^{k}}\)

Questions & Answers

QUESTION:

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

\(\sum_{k=0}^{\infty} \frac{x^{k}}{2^{k}}\)

ANSWER:

Solution 49E
Step 1:

 is an infinite geometric series where and .

So,


As we know that sum of an infinite geometric series is
where .

Using for the given power series, we get

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