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.

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 $\displaystyle \frac{20\cdot n!}{(n+1)!}=\frac{20}{n+1}$.

But is it meant to be $\displaystyle \frac{(20n)!}{(n+1)!}~?$

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)?

Re: Help with factorial limit

(20 x n(n-1)...1)/1x2x3x4x...n(n+1) = 20/(n+1) after simplification its easy.

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)?

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