# Simplify the factorial expression

• Sep 26th 2009, 09:05 PM
flexus
Simplify the factorial expression
Simplify the factorial expression

(3n + 1)! / (3n)! and (n+2)! / n!

ok i know how to simplify 4!/6! which is 1/30 but when they have the letter n in the problem i dont know where to start. man im getting tire been at this since 4 pm lol
• Sep 26th 2009, 09:14 PM
Chris L T521
Quote:

Originally Posted by flexus
Simplify the factorial expression

(3n + 1)! / (3n)! and (n+2)! / n!

ok i know how to simplify 4!/6! which is 1/30 but when they have the letter n in the problem i dont know where to start. man im getting tire been at this since 4 pm lol

$\frac{(3n+1)!}{(3n)!}=\frac{(3n+1){\color{red}(3n) (3n-1)\cdots(2)(1)}}{(3n)!}=\frac{(3n+1)\cdot(3n)!}{(3 n)!}=3n+1$.

Does this make sense?

Try to do something similar for the second one.
• Sep 26th 2009, 09:23 PM
flexus
Quote:

Originally Posted by Chris L T521
$\frac{(3n+1)!}{(3n)!}=\frac{(3n+1){\color{red}(3n) (3n-1)\cdots(2)(1)}}{(3n)!}=\frac{(3n+1)\cdot(3n)!}{(3 n)!}=3n+1$.

Does this make sense?

Try to do something similar for the second one.

ok i see that the (3n)! canceled out but how did you get (3n)(3n-1)...(2)(1) and then where did it go??
• Sep 26th 2009, 09:26 PM
Chris L T521
Quote:

Originally Posted by flexus
ok i see that the (3n)! canceled out but how did you get (3n)(3n-1)...(2)(1) and then where did it go??

I got that because that is how factorial is defined!

$(3n+1)!=(3n+1)(3n)(3n-1)(3n-2)\cdots(3)(2)(1)$

But that's the same as saying $(3n+1)!=(3n+1)\cdot(3n)!$ - Hence why we got cancellation towards the end of the problem.
• Sep 26th 2009, 09:31 PM
flexus
Quote:

Originally Posted by Chris L T521
I got that because that is how factorial is defined!

$(3n+1)!=(3n+1)(3n)(3n-1)(3n-2)\cdots(3)(2)(1)$

But that's the same as saying $(3n+1)!=(3n+1)\cdot(3n)!$ - Hence why we got cancellation towards the end of the problem.

your probably gonna get angry if i told you i didnt understand that so im gonna go youtube factorials and ill get back to this problem. thank you for trying to explain. your help was greatly appreciated.
• Sep 27th 2009, 03:37 AM
mr fantastic
Quote:

Originally Posted by Chris L T521
I got that because that is how factorial is defined!

[snip]

And defined! = (defined)(efined)(fined)(ined)(ned)(ed)(d)