0.3. The Fibonacci numbers Fo, Fi, F2,., are defined by the rule Fo=0, F1 = 1, Fn-Fn-1 + Fn-2. In this problem we will confirm that this sequence grows exponentially fast and obtain some bounds on its growth (a) Use induction to prove that F 2 5n for n6 (b) Find a constant c1 such that Fn s 2cn for all n 2 0. Show that your answer is correct. (c) What is the largest c you can find for which Fn-(25")