0.3. The Fibonacci numbers Fo, F1, 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 En > 20.5n for n > 6. (b) Find a constant c 0. Show that your answer is correct. (c) What is the largest c you can find for which Fn = N(2n)