Calculating (n+2)! quickly and accurately - Help Needed!

[Phyzwizz]

I know that n!=(1)(2)(3)...(n-1)(n)
I am confused how I can figure out what (n+2)! is in order to divide it by n!
How can I figure (n+2)! out and what is it, so that I won't have to ask if what I got is right.

Thanks!

 

[SteamKing]

You have already written out the expansion for n!. Now, if you add 1 to n, what additional term must be included in n! to make it (n+1)! Once you figure this out, repeat to find
(n+2)!

 

[Mentallic]

3!=3*2*1
4!=4*3*2*1
10!=10*9*8*...*2*1
etc.
What is 10! divided by 8! then?

 

[Phyzwizz]

oh okay so (n+2)! would be (1)(2)(3)...(n-1)(n)(n+1)(n+2)?

 

[SteamKing]

Right. Now figure your quotient (n+2)!/n!.

 

[Mark44]

oh okay so (n+2)! would be (1)(2)(3)...(n-1)(n)(n+1)(n+2)?

Which is the same as (n + 2)(n + 1) n!, right?

 

[SteamKing]

There is no n! in the quotient of (n+2)!/n!. Remember the expansion of (n+2)! is
(n+2)(n+1)n!. Dividing (n+2)! by n! is (n+2)(n+1)n!/n! = (n+2)(n+1).