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!
Wed Jul 10 13:02:07 MDT 1996
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