1/(2-1)(2+1)+1/(3-1)(3+1)+1/(4-1)(4+1)+...+1/(n-1)(n+1)
=1/2[1-1/3+1/2-1/4+1/3-1/5+1/4-1/6+...+1/(n-1)-1/(n+1)]
=1/2[1-1/(n+1)]
=n/[2(n+1)]