因为1/n(n+2)=1/2*[1/n-1/(n+2)]
所以 1/1×3＋1/2×4+1/3×5+……1/n(n+2),
=1/2*[1-1/3+1/2-1/4+1/3-1/5+.+1/(n-1)-1/(n+1)+1/n-1/(n+2)]
=1/2*[1+1/2-1/(n+1)-1/(n+2)]
=3/4-1/2(n+1)-1/2(n+2)