2 (15 points). Let f(x) = 1- r (a) Express x f (x) = 1 - T as a power series on the interval (-1, 1). 1 (b) Find a power series expression for f'(x) = (1 -x)2 on (-1, 1). (c) Use the result of (b) to find the sum of the series DO n+1 CIT = 1+1+ + + J.. . 2n 16 32 n=0