5. Prove that 12 + 32 + 52 + ... + (2n + 1)2 = (n + 1) (2n+ 1)(2n + 3) /3 whenever n is a nonnegative integer. 6. Prove that 1 . 1! + 2 . 2! + ... + n . n! = (n+ 1)!-1 whenever n is a positive integer.3. Let P(n) be the statement that 12 + 2- + ... + n- = n(n + 1)(2n + 1) /6 for the positive integer n. a) What is the statement P(1)? b) Show that P(1) is true, completing the basis step of a proof that P(n) is true for all positive integers n. c) What is the inductive hypothesis of a proof that P(n) is true for all positive integers n? d) What do you need to prove in the inductive step of a proof that P(n) is true for all positive integers n? e) Complete the inductive step of a proof that P(n) is true for all positive integers n, identifying where you use the inductive hypothesis. f) Explain why these steps show that this formula is true whenever n is a positive integer