Power Series


\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 tex2html_wrap_inline158 yields tex2html_wrap_inline160 , consequently C=0 and we are done:


By inspection, the center of the power series is tex2html_wrap_inline158 ; you should expect this formula to be valid for |x|<1. Why?

Where to go next?

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

Helmut Knaust
Wed Jul 10 13:02:07 MDT 1996
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