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For each positive integer n , let P ( n ) be the inequality 2 n < ( n + 1)!. (a) Write P (2).

For each positive integern, letP(n)

be the inequality

2ⁿ< (n+ 1)!.

(a)

WriteP(2).

(b)

WriteP(k).

(c)

WriteP(k+ 1).

(d)

In a proof by mathematical induction that this inequality holds for every integern2,

what must be shown in the inductive step?

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