nx+(n+1)y=根号2
nx + (n+1)y
—————— = 1
根号2
(n/根号2)x + [(n+1)/根号2]y = 1
得到直线的横截距为2=根号2/n,纵截距为根号2/(n+1)
那么Sn=根号2/n*根号2/(n+1)*0.5=1/n(n+1)
那么S1+……+S2000
1/(1*2)+1/(2*3)+1/(3*4)+……+1/(2000*2001)
=1/2+1/2-1/3+1/3-1/4+……+1/2000-1/2001（小学学过的一种方法）
=2000/2001