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

1 Answer
Nov 24, 2015

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

Explanation:

Remembering that we can write:
n! =n*(n-1)!n!=n(n1)!

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