Let P(n) be the statement 3n < n!.For n = 1,3n = 3 × 1 = 3n! = 1! = 1Now, 3 > 1So, P(1) is not true.For n = 2,3n = 3 × 2 = 6n! = 2! = 2Now, 6 > 2So, P(2) is not true.For n = 3,3n = 3 × 3 = 9n! = 3! = 6Now, 9 > 6So, P(3) is not true.For n = 4,3n = 3 × 4 = 12n! = 4! = 24Now, 12 < 24So, P(4) is true.For n = 5,3n = 3 × 5 = 15n! = 5! = 120Now, 15 < 120So, P(5) is true.Similarly, it can be verified that 3n < n! for n = 6, 7, 8, ... .Thus, the statement P(n) : 3n < n! is true for all n ≥ 4 but P(1), P(2) and P(3) are not true.