# Help with factorial limit

• Apr 14th 2013, 11:48 AM
Help with factorial limit
Okays so, I have the limit as n-> infinity: (20n!)/((n+1)!)

My first thought is that you would divided all terms by n, basically making the limit = 20!/1!, which is just 20!... but I don't think that this is correct. What do you guys think?

Thanks.
• Apr 14th 2013, 12:02 PM
Plato
Re: Help with factorial limit
Quote:

Originally Posted by Shadow236
Okays so, I have the limit as n-> infinity: (20n!)/((n+1)!)

Well, if it as you posted it $\frac{20\cdot n!}{(n+1)!}=\frac{20}{n+1}$.

But is it meant to be $\frac{(20n)!}{(n+1)!}~?$
• Apr 14th 2013, 12:14 PM
Re: Help with factorial limit
It should be the first way you have it. If that's so, how do you get to 20/(n + 1)?
• Apr 14th 2013, 12:19 PM
MINOANMAN
Re: Help with factorial limit
(20 x n(n-1)...1)/1x2x3x4x...n(n+1) = 20/(n+1) after simplification its easy.
• Apr 14th 2013, 12:34 PM
Plato
Re: Help with factorial limit
Quote:

Originally Posted by Shadow236
It should be the first way you have it. If that's so, how do you get to 20/(n + 1)?

$(n+1)!=(n+1)(n!)$