Question

Let P (n): 2n < (1 × 2 × 3 × … × n). Then the smallest positive integer for which P(n) is true is 

A. 1 

B. 2 

C. 3 

D.4

Answer 1

Given P(n):2n< (1×2×…. ×n)

For n=1, 2<2 

For n=2, 4<4 

For n=3, 6<6 

For n=4, 8<24 

∴ the smallest positive integer for which P(n) is true is 4.