- #1

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## Homework Statement

Use M.I. to prove that n! > n^3 for n > 5

## The Attempt at a Solution

I already proved n! > n^2 for n>4, but this is nothing like that.

This is my inductive step so far.

n=k+1

(k+1)! > (k+1)^3

(k+1)! - (k+1)^3 > 0[/B]

**(k+1)! - (k+1)^3 = (k+1)[k! - (k+1)^2]**

**> (k+1)[k^3 - (k+1)^2]**

This is how far I can get, any hints? Am I going in the right track or am I going in the wrong direction completely?

This is how far I can get, any hints? Am I going in the right track or am I going in the wrong direction completely?