Teoria Fatorial

$ \begin{align}\dfrac{n!}{(n- 2)!} &= \dfrac{n \cdot (n-1)!}{(n- 2)!} = \\
&= \dfrac{n \cdot (n-1) \cdot (n-2)!}{(n- 2)} = \\
&= n \cdot (n-1) = \\
&= n^2- n \end{align}$

$ \begin{align} \dfrac{(n-1)!} {(n+1)!} &= \dfrac{(n-1)!} {(n+1) \cdot n!} = \\
&= \dfrac{(n-1)!} {(n+1) \cdot n \cdot (n-1)!}= \\
&= \dfrac{1}{(n+1) \cdot n}\end{align}$