proof

Quote:

Originally Posted by Mhmh96

How to prove that:
http://im24.gulfup.com/2012-05-06/1336294097491.jpg

Note that $\sum\limits_{k = 1}^5 {k!} = 153$ is a multiple of nine.

Also, if $N\ge 6$ then $6!={\color{blue}6}\cdot 5\cdot 4\cdot{\color{blue}3}\cdot 2={\color{blue}720}$ which is a multiple of nine.

If $N\ge 6$ then $N!$ is a multiple of nine. WHY?