Solution Found!
Answer: Combining power series Use the geometric series to
Chapter 8, Problem 24E(choose chapter or problem)
Combining power series Use the geometric series
\(f(x)=\frac{1}{1-x}=\sum_{k=0}^{\infty} x^{k}\), for |x| < 1,
to find the power series representation for the following functions (centered at 0). Give the interval of convergence of the new series.
\(f\left(x^{3}\right)=\frac{1}{1-x^{3}}\)
Questions & Answers
QUESTION:
Combining power series Use the geometric series
\(f(x)=\frac{1}{1-x}=\sum_{k=0}^{\infty} x^{k}\), for |x| < 1,
to find the power series representation for the following functions (centered at 0). Give the interval of convergence of the new series.
\(f\left(x^{3}\right)=\frac{1}{1-x^{3}}\)
ANSWER:Solution 24EStep 1:We are given the geometric series for Therefore the interval of convergence is (-1,1)We are asked to find the power series representation of with centre 0.