Question

How do you simplify `((2n+2)!)/((2n)!)`?

Answer 1

I found: `(2n+2)(2n+1)`

Explanation:

Remembering that we can write:
`n! =n*(n-1)!`

we have (applying twice the above property to the numerator):
`((2n+2)!)/((2n)!) =((2n+2)(2n+1)cancel((2n)!))/(cancel((2n)!))=(2n+2)(2n+1)`

Check with `n=3`
`((2n+2)!)/((2n)!) =(8!)/(6!)=40320/720=56`
and:
`(2n+2)(2n+1)=8*7=56`