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Combining power series Use the power series representation
Chapter 8, Problem 28E(choose chapter or problem)
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.
\(g(x)=x^{3} \ln (1-x)\)
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.
\(g(x)=x^{3} \ln (1-x)\)
ANSWER:Solution 28E
Step 1:
Given
Using the power series representation for , we get