How to prove that:

http://im24.gulfup.com/2012-05-06/1336294097491.jpg

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- May 6th 2012, 04:55 AMMhmh96proof
How to prove that:

http://im24.gulfup.com/2012-05-06/1336294097491.jpg - May 6th 2012, 07:45 AMPlatoRe: proof
Note that $\displaystyle \sum\limits_{k = 1}^5 {k!} = 153$ is a multiple of nine.

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

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