Power Series

Integrate

$\begin{displaymath}\frac{d\ln(x+1)}{dx} = \frac{1}{1-(-x)}\end{displaymath}$

on both sides and use the geometric series formula on the right to obtain

Performing the integration term by term on the right side you obtain

Plugging in the center yields , consequently C=0 and we are done:

By inspection, the center of the power series is ; you should expect this formula to be valid for |x|<1. Why?

Continue with the concept of the radius of convergence of a power series next!

Helmut Knaust
Wed Jul 10 13:02:07 MDT 1996
This module consists of 4 HTML pages.