# Thread: Recusive Definition

1. ## Recusive Definition

I am really confused on how to do recursive definitions. The question is:

n! >= 3^n for every Integer n >=7

The textbook I have really doesn't explain how to solve for it and I am hoping someone can explain how I prove for it. can someone please explain how you solve for these type of equations? Thanks!

EDIT: I forgot to mention that we are using Mathematical Induction.

2. Originally Posted by Phat32
I am really confused on how to do recursive definitions. The question is:

n! >= 3^n for every Integer n >=7

The textbook I have really doesn't explain how to solve for it and I am hoping someone can explain how I prove for it. can someone please explain how you solve for these type of equations? Thanks!

EDIT: I forgot to mention that we are using Mathematical Induction.
Use induction with $\displaystyle n=7$ as a base case, then show that if for some $\displaystyle k$:

$\displaystyle k!\ge 3^k$

then

$\displaystyle (k+1)! \ge 3^{k+1}$

CB