How do you simplify ((n+1)!)/((n-2)! )?

1 Answer
Mar 2, 2018

n^3-n

Explanation:

The numerator can be rewritten as:

((n+1) * (n+1-1) * (n+1-2) * (n+1-3)!)/((n-2)!)

Simplifying:

((n+1) * (n) * (n-1) * (n-2)!) / ((n-2)!)

We can cancel the (n-2)! values out:

(n+1)(n-1)(n)

=n^3-n

And there we have our answer.