65. Suppose that the coefficients of F(x) = anx" are periodic; that is, for some whole number M > 0, n=0 we have aM+n = an. Prove that F(x) converges absolutely for |x| < 1 and that ao +ajx + ...+ aM-1xM-1 1- xM F(x) Hint: Use the hint for Exercise 53.

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