Problem 1. Recall that 1 >r" = 1+x + x2 + x³ + .. (1) %3D 1- x n=0 for all -1 < x < 1. (a) Show that () = (don't overthink it – just differentiate like in Calc I). (b) Using (1), find a power series expansion for y centered at 0. What is the radius of convergence of the power series? (c) Find a power series expansion for 7 z centered at 0. What is the radius of convergence of the power series? %3D

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