sn=1/2+1/6+1/12+.+1/nx(n+1)=
=1/1x2+1/2x3+1/3x4+.+1/nx(n+1)=
=1-1/2+1/2-1/3+1/3-1/4+.+1/n-1/(n+1)=
=1-1/(n+1)=n/(n+1)