Let P(n) be the statement that 1² + 2²+ …. + n²=n(n + 1)(2n + 1)/6 for the positive integer n. a) Show that P(1) is true, completing the basis step of a proof that P(n) is true for all positive integers n. b) What is the inductive hypothesis of a proof that P(n) is true for all positive integers n? c) What do you need to prove in the inductive step of a proof that P(n) is true for all positive integers n? d) 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) Explain why these steps show that this formula is true whenever n is a positive integer.

Solved: Let P(n) be the statement that 1² + 2²+ …. + n²=n(n + 1)(2n + 1)/6 fo

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let pn be the statement that 12 22 n2nn 12n 16 for the positive intege

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Let P(n) be the statement that 1² + 2²+ …. + n²=n(n + 1)(2n + 1)/6 for the positive integer n. a) Show that P(1) is true, completing the basis step of a proof that P(n) is true for all positive integers n. b) What is the inductive hypothesis of a proof that P(n) is true for all positive integers n? c) What do you need