Chapter 9.2, Problem 39E

Combining power series Use the power series representation

$f(x)=\ln (1-x)=-{\displaystyle \underset{k=1}{\overset{\infty }{\sum }}\frac{x^k}{k},\text{for}-1\le x<1,}$

to find the power series for the following functions (centered at 0). Give the interval of convergence of the new series.

39. p(x) = 2x⁶ ln (1 − x)