4 Consider the open sentence Pn 7 4 Consider the open sente

4. Consider the open sentence P(n): !> (7 4. Consider the open sentence P(n): n! fornEN for n N. for nEN Prove or disprove: Vn E N, P(n) Prove or disprove: Vn E N. P(n

Solution

it is false

since (n!/n^n) approaches zero as n goes to infinity

take n = 6

6! = 720

3^6 = 729

6! < (6/2)^6