+26393 Compute
\(\mathbf{\dfrac{(n-1)!n}{(n+1)!}}\)
\(\begin{array}{|rcll|} \hline && \mathbf{\dfrac{(n-1)!n}{(n+1)!}} \quad | \quad \boxed{(n-1)!n = n!} \\ &=& \dfrac{n!}{(n+1)!} \quad | \quad \boxed{n!(n+1) = (n+1)!} \\ &=& \dfrac{n!}{n!(n+1)} \\ &=& \mathbf{\dfrac{1}{ n+1 }} \\ \hline \end{array} \)
+26393 Compute
\(\mathbf{\dfrac{(n-1)!n}{(n+1)!}}\)
\(\begin{array}{|rcll|} \hline && \mathbf{\dfrac{(n-1)!n}{(n+1)!}} \quad | \quad \boxed{(n-1)!n = n!} \\ &=& \dfrac{n!}{(n+1)!} \quad | \quad \boxed{n!(n+1) = (n+1)!} \\ &=& \dfrac{n!}{n!(n+1)} \\ &=& \mathbf{\dfrac{1}{ n+1 }} \\ \hline \end{array} \)
