Question 1 (Fibonacci Numbers, 10 points). Suppose that we have a sequence Fn defined by Fi = F= 1 and for n 3 we have that Fn = Fn-1 + Fn-2 Consider the following purported proof that Fn =O (1) by induction: If n = 1, then F = 1 = 0 (1). If n = 2, then F = 1 = 0 (1). Otherwise, assuming that Fm = 0 (1) for all m