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Power series from the geometric series Use the geometric I
Chapter 1, Problem 21RE(choose chapter or problem)
QUESTION:
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.
\(f(x)=\frac{1}{1-x^{2}}\)
Questions & Answers
QUESTION:
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.
\(f(x)=\frac{1}{1-x^{2}}\)
ANSWER: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