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gselm
gselm
05.11.2019 • 
Mathematics

Let p(n) be the statement that 1^2 + 2^2 +⋯+ n^2 = 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.

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