[latex] \frac{(n-1)!}{n!`} - \frac{n!}{(n+1)!} [/latex]

(n-1)!/[(n-1)!*n]-n!/[n!(n+1)]=1/n-1/(n+1)=(n+1-n)/[n(n+1)]=1/(n²+n)

n!=1*2*3*....*(n-1)*n n!/(n-1)!=n (n-1)!/n!=1/n --------------------------- [latex] \frac{(n-1)!}{n!} - \frac{n!}{(n+1)!} = \frac{1}{n} - \frac{1}{n+1} = \frac{n+1-n}{n(n+1)} = \frac{1}{n(n+1)} [/latex]