Taylor series. Consider a real number s ER No and the function x + (1+x)³. We want to show that the Taylor series of this function about x = 0 is given by f(x) = [ (i) z², Σ(;) (0) - Σ (a) Show that the given series has a radius of convergence R = 1. (c) Consider the function (b) Show that f satisfies (1+x) f'(x) = sf(x). (s-k+ 1)(s-k+2)...s f(x) (1+x)*' g(x) = Show that g is constant and deduce that |x| < f(x) = (1+x)" . (Total: k! ¹