Question

Prove by induction: n! > 2^n for all n>/=4

Answer 1

step one: show that , it's true when n =4 ==> 4! =24 , 2^4=16 ==> it's true

Answer 2

step two : assume it's true when n=k ===> k!>2^k

Answer 3

step three: show that it's true when n=k+1 ==> (k+1)! =(k+1) k! , 2^(k+1) = 2^k *2 ==> (k+1)!>2^(k+1) is true ==> n! > 2^n for all n>/=4