## Example 8.3.12 (d): Differentiating and Integrating Power Series

Find, with proof, a power series centered at

*c = 0*for the function*f(x) =*, for^{1}/_{(1-x)2}*-1 < x < 1*.We need to resort to information we already know. We did discuss the geometric series:

^{1}/_{1-x}= x^{n}

Differentiating both sides finishes the problem:

f(x) ==^{1}/_{(1-x)2}^{1}/_{1-x}= x^{n}= nx^{n-1}

n x^{n-1}f(x) =^{1}/_{(1-x)2}