Solution Found!
Solution: Combining power series Use the power series
Chapter 8, Problem 30E(choose chapter or problem)
Combining power series Use the power series representation
\(f(x)=\ln (1-x)=-\sum_{k=1}^{\infty} \frac{x^{k}}{k), for \(-1 \leq x<1\),
to find the power series for the following functions (centered at 0). Give the interval of convergence of the new series.
\(f\left(x^{3}\right)=\ln \left(1-x^{3}\right)\)
Questions & Answers
QUESTION:
Combining power series Use the power series representation
\(f(x)=\ln (1-x)=-\sum_{k=1}^{\infty} \frac{x^{k}}{k), for \(-1 \leq x<1\),
to find the power series for the following functions (centered at 0). Give the interval of convergence of the new series.
\(f\left(x^{3}\right)=\ln \left(1-x^{3}\right)\)
ANSWER:Solution 30E
Step 1:
Given
Using the power series representation for , we get