The Fibonacci numbers are: 1, 1, 2, 3, 5, 8, 13, 21, 34, .... In general, the Fibonacci numbers are defined by f sub(1) = 1, f sub(2) = 1, and for n>or= 3, f sub(n) = f sub(n-1) + f sub(n-2). Prove that the nth Fibonacci number f sub(n) satisfies f sub(n) < 2^n.