The Fibonacci numbers F_0, F_1, F_2, are defined by the following rule: F_0 = 0, F_1 = 1, F_n = F_n - 1 + F_n - 2. In this problem, we will see that this sequence grows exponentially fast. We will also establish some bounds on its growth. a) Use induction to prove that F_n greaterthanorequalto 2^0.5n for n greaterthanorequalto 6. b) Find a constant c