Q: Let P(n) be the statement that 13 + 23+….n3 = (n(n + 1) / 2)² for the positiveinteger n. a.) What is the statement P(1)? b.) Showthat P(1), completing the basis step of theproof? c.) What is the Inductive Hypothesis? d.) What do you need to prove in the Inductive Step? e.) Complete the inductive Step? f.) Explain why these steps show that the formula is true whenevern is a positive integer ____________________________________________________________________________ What I have: a.) P(n) = (n(n + 1) / 2)² P(1) = (1(1 + 1) / 2)² = (2 / 2)² = 1 b.) Basis Step: wewill let n = 1 n3 = (n(n + 1) / 2)² 13 = (1(1 + 1) / 2)² 1 = (2 / 2)² 1 = 1 Since bothare equal, the basis step hold. c.) Inductive Hypothesis: This is the statement 13 + 23+….k3 = (k(k + 1) / 2)² d.) I have to prove that k > 1 and P(k) implies P(k +1). Or. 13 + 23 +….k3 + (k +1)3 = ((k + 1)((k + 1) + 1) / 2)² e.) ?
