设S1=1＋1／1∧2+1/2∧2，S2=1+1/2∧2+1/3∧2，S3=1+1/3∧3+1/4∧2，…，Sn=1+1/n∧2＋1
设S1=1＋1／1∧2+1/2∧2，S2=1+1/2∧2+1/3∧2，S3=1+1/3∧3+1/4∧2，…，Sn=1+1/n∧2＋1
日期：2014-03-18 23:05:47 人气：1
∵sn=1+[n^2+(n+1)^2]/[n²(n+1)²]=(n^2+n+1)^2/[n²(n+1)²]
∴√sn=（n^2+n+1)/[n(n+1)]=1+1/n-1/(n+1)
∴s=(1+1-1/2）+（1+1/2-1/3)+(1+1/3-1/4)+……+[1+1/n-1/(n+1)]
=n+(1-1/2+1/2-1/3+1