Mathematics > QUESTION PAPER (QP) > MATHEMATICS STUDY MATERIAL (QUESTIONS ONLY) (All)
MATHEMATICS STUDY MATERIAL (QUESTIONS ONLY)
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Exercise 4, Sec 5.1, 8th edition Let P(n) be the statement that 13 + 23 + . . . + n 3 = (n(n + 1)/2)2 for the positive integer n. a) What is the statement P(1)? b) Show that P(1) is true, complet... ing the basis step of the proof of P(n) 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. [Show More]
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