Power Series
Integrate
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?
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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