Chapter 9.2, Problem 41E

Differentiating and integrating power series Find the power series representation for g centered at 0 by differentiating or integrating the power series for f (perhaps more than once). Give the interval of convergence for the resulting series.

41. $g(x)=\frac{2}{{(1-2x)}^2}$ using $f(x)=\frac{1}{1-2x}$