根据:1/n(n+1)=1/n-1/(n+1)1/1*2+1/2*3+1/3*4+.1/n(n+1)=1/1-1/2+1/2-1/3+1/3-1/4+.+1/(n-1)-1/n+1/n-1/(n+1)=1-1/(n+1)=n/(n+1)所以sn=1/（1*2）+1/(2*3)+1/（3*4）+……+1/(n(n+1))=n/(n+1)