1/n(n+1)=[(n+1)-n]/n(n+1)=1/n-1/(n+1)
∴Sn=1-1/2+1/2-1/3+1/3-1/4+…+1/n-1/(n+1)
=1-1/(n+1)
=n/(n+1)
ps:分式不会打出来……勉强看吧……