I: Induction (40 pt.) (40 pt., 10 pt. each) Prove each of the following statements using induction. For each statement, answer the following questions a. b. c. d. e. What is the base case? Complete the basis step of the proof by showing that the base case is true What is the inductive hypothesis? What do you need to show in the inductive step of the proof? Complete the inductive step of the proof Prove that .1 2n+1 + (-1) 3 2 -5 j=0 for any nonnegative integer n . Prove that n! 1 . Let ao, a1, a2, be the sequence defined by the following recurrence relation ai = 4 + a1-1 for i21 Prove that an >4n for any nonnegative integer n . Prove that n3 2n is divisible by 3 for any positive integer n