Use mathematical induction to prove

Question

Prove that n! > 2ⁿ is true for every positive integer n >(or equal to) 4 using mathematical induction

Answer 1

5! = 120 > 32 = 2^5

Given: n! > 2^n

(n+1)! = n * n!

> n * 2^n <--- by induction hypothesis

> 2 * 2^n <---- n>4

= 2^(n+1)