What Are the Key Representations of Factorials n!, (n+1)!, and (n-1)!?

[nameVoid]

Id like to know some basic representations of factorials n!, (n+1)!,(n-1)! ext..

 

[rasmhop]

What exactly do you want? When you say representations do you have anything particular in mind? I can easily provide you with:
$$n! = n\times(n-1)! \qquad \mbox{for }n > 1$$
but I'm suspecting you're looking for something a bit more interesting than that.

 

[VeeEight]

You might find Wilson's Theorem interesting.
Combinatorial math is an interesting field where you deal a lot with factorials and their properties. Sometimes the algebra is tedious but you get interesting and useful results. Even if you don't know any group theory, everyone has seen basic counting in the form of permutations.

If you had a specific problem then do post it.

 

[nameVoid]

n!=n(n-1)!
(n+1)!=n!(n+1)?
(2n+4)!=(2n+4)(2n-3)!
(2n)!=2n(2n-1)!
..?

 

[The Chaz]

n!=n(n-1)!
(n+1)!=n!(n+1)?
(2n+4)!=(2n+4)(2n-3)!
(2n)!=2n(2n-1)!
..?

Yeah, but all of that just follows from the first line.
Check out http://en.wikipedia.org/wiki/Binomial_coefficient#Recursive_formula"

The binomial coefficient ("choose function", or "nCr") is where you'll see factorials most often, at least until you solve the Reimann-zeta hypothesis.

 

[Mark44]

n!=n(n-1)!
(n+1)!=n!(n+1)?
(2n+4)!=(2n+4)(2n-3)!
(2n)!=2n(2n-1)!
..?

Probably a typo, but (2n+4)!=(2n+4)(2n+3)!, not (2n + 4)(2n - 3)! as you had.