Solution Found!
Answer: Combining power series Use the power series
Chapter 8, Problem 29E(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.
h(x) = x In (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.
h(x) = x In (1 – x)
ANSWER:Solution 29EStep 1:Given Using the power series representation for , we get