Factorials

5! = 5 _ 4 _ 3 _ 2 _ 1

0! = 1

Canceling Out Factorials

Bigger factorial overshoots the smaller one by some numbers and that is the remaining factors.

8!/10! = 8!/(8! * 9 * 10) = 1/(10*9)

Simplifying

n!/(n+2)! = 1/[(n+1)(n+2)]