Let P(n) be the statement that 1² +2²+...+ n² = 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? Complete the inductive step of a proof that P(n) is true for all positive integers n, identifying where you use the inductive hypothesis. e) f) Explain why these steps show that this formula is true whenever n is a positive integer.

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