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Representing functions by power series Identify the
Chapter 8, Problem 49E(choose chapter or problem)
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