How Does ((n+1)^2 * n!) / ((n+1)! * n^2) Simplify to (n+1) / n^2?

[Helge]

How can ((n+1)^2(*n!))/((n+1)!*n^2) be simplified to (n+1)/n^2?

My own answer is (n+1)^2/n^2, but its apparently wrong

 

[DivisionByZro]

Here's how:

$$\frac{(n+1)^{2}\cdot n!}{(n+1)!\cdot n^{2}} = \frac{(n+1)^{2}\cdot n!}{(n)!\cdot(n+1) \cdot n^{2}} = \frac{(n+1)\cdot n!}{(n)! \cdot n^{2}} = \frac{(n+1)}{n^{2}}$$

All you had to do was expand the (n+1)! into (n+1)n!.

:)