Simplifying Factorials: How to Simplify 2n+2!?

[xXOfNiRXx]

Just a quick question. I'm having problems with factorials. For example, how do you simplify 2n+2!? Is it 2n!*2n+1!?

Thanks everybody!

 

[Mark44]

Strictly speaking, 2n + 2! would be just 2n + 2, since 2! = 2. You probably meant (2n + 2)!, which is (2n + 2)*(2n + 1)*(2n)!.

Edit: added a missing factor in the above.


Note that 2n! is different from (2n)!. The first is 2(n*(n-1)*(n-2)*...*2*1). The second is 2n*(2n-1)*(2n-2)*...*2*1.

You should get into the habit of using parentheses...

 

[Avodyne]

You probably meant (2n + 2)!, which is (2n + 1)*(2n)!.

Actually, it's (2n+2)*(2n+1)*(2n)!, but I'm sure you knew that.

 

[Mark44]

Yeah, knew that, but didn't manage to write it.
I edited my earlier post.