Consider the series f(x) = 1 - 1/2(x - 3) + 1/4 (x - 3)² - 1/8 (x - 3)³ + ....
(a) For what values of x does the series converge?
(b) What is the sum of the series?
(c) Find a power series representation for f'(x).
(d) For what values of x does the f' series converge?
(e) Find the sum of the f' series. Let f(x) = 1/(1 - x).