Verified answer

[tex]\displaystyle (\frac{1}{n!}-\frac{1}{(n+1)!})*n!=(\frac{1}{n!}-\frac{1}{(n+1)*n!})*n!=\frac{n+1-1}{(n+1)*n!}*n!=\frac{n}{n!(n+1)}*n!=\\\\\frac{n}{(n+1)!}*n!=\frac{n}{(n+1)*n!}*n!=\frac{n}{n+1}[/tex]