For each positive integer n, let P(n) be the property 2n <

Chapter 5, Problem 7E

(choose chapter or problem)

For each positive integer n, let P(n) be the property 2n < (n + 1)!.a. Write P(2). Is P(2) true?b. Write P(k).c. Write P(k + 1).d. In a proof by mathematical induction that this inequality holds for all integers n ? 2, what must be shown in the inductive step?

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