1. The problem statement, all variables and given/known data Show that n^3 < n! for all n >= 6. 2. Relevant equations 3. The attempt at a solution We see that for the base case of n = 6, the claim holds. Suppose that k^3 < k! for some natural number k >= 6. Consider that: (k+1)^3 = k^3 + 3k^2 + 3k + 1 < k! + 3k^2 + 3k + 1 [By induction hypothesis] What's a neat way to finish this? I'm a bit rusty, apparently.