If ( P(n): 2^ n < n ! ) then the smallest positive integer for which ( P(n) ) is true, is

Step-by-step solution

P( n ): 2^ n Since P(1): 2 < 1 is false. P(2): 2² < 2 ! is false P(3): 2³ < 3 ! is false P(4): 2⁴ < 4 ! is true. P(5): 2⁵ < 5 ! is true. So, the smallest positive integer is 4 .