∵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+1/3-1/4+……+1/n-1/(n+1))
=n+(1-1/(n+1))=n+1-1/(n+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+1/3-1/4+……+1/n-1/(n+1))
=n+(1-1/(n+1))=n+1-1/(n+1)