Math Help - Simplify the factorial expression

1. 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

2. 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.

3. 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??

4. 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.

5. 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.

6. 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)