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(1) Suppose that the power series f (.r) = has a finite radius of convergence R > O. Prove that for any xo e

(1) Suppose that the power series f (".r) = has a finite radius of convergence R > O. Prove that for any xo e ( R, R.) there exists a sequence {bn} such that f (x) bn('.r where the new series has a radius of convergence p R (5 pts)

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