a) Semplificare l’espressione $\displaystyle \frac{n!}{(n-2)!}$.

Soluzione.
$\displaystyle \frac{n!}{(n-2)!}=\frac{n(n-1)(n-2)!}{(n-2)!}=n(n-1)=n^2-n$.

b) Semplificare l’espressione $\displaystyle \frac{(n-1)!}{(n-2)!}\cdot (n-1)$.

Soluzione.

$\displaystyle \frac{(n-1)!}{(n-2)!}\cdot (n-1)=\frac{(n-1)\cdot (n-2)!}{(n-2)!}\cdot (n-1)=$

$\displaystyle =(n-1)^2=n^2-2n+1$.