8n divides (4n)! Proof by induction

1. Dec 7, 2008

kathrynag

1. The problem statement, all variables and given/known data
I need to do this by proof by induction
8n divides (4n)!

2. Relevant equations

3. The attempt at a solution
I already did it for 1, now I need to do for k and k+1
(4k)!t=8k

2. Dec 7, 2008

mutton

If 8k divides (4k)!, how can 8k be a multiple of (4k)! as you wrote?

3. Dec 7, 2008

kathrynag

$$8^{k}$$ divides (4k)!
$$8^{k}$$*t=(4k)!

4. Dec 7, 2008

mutton

Simplify (4(k + 1))! in terms of (4k)!

5. Dec 7, 2008

kathrynag

(4k+4)!=(4k+4)(4k+3)(4k+2)(4k+1)(4k)!

6. Dec 7, 2008

mutton

You already know that $$8^k$$ divides (4k)!, so does 8 divide everything else?

7. Dec 7, 2008

Yes....

8. Dec 7, 2008

mutton

Then you have all the details for the complete proof.

9. Dec 7, 2008

kathrynag

Ok, I see....