Hint for Section 4.3 Question 2

2. Let P(n) be the claim that   n! > 2ⁿ for all integers n4.

P(4) is the statement: 4! > 2⁴.

P(k) is the statement:  k! > 2^k.

P(k+1) is the statement: (k + 1)! > 2^k+1.

For a proof by induction, you first need to check that the statement P(4) is true. Then assume that P(k) is true and use this to show that P(k + 1) is true.

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