Prove by induction the following proposition: Proposition: The Fibonacci sequence 1, 1, 2, 3, 5, 8, 13, . . . is defined as a sequence whose two first terms are F(1) = 1, F(2) = 1 and each subsequent term is the sum of the two previous ones: F(n) = F(n1) + F(n2), for n > 2. Prove that F(n) < 2^n for every n 1.