1/(1×2)+1/(2×3)+1/(3×4)+1/(4×5)+...+1/(99×100)=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/99-1/100=1-1/100=99/100 一般的：1/[n(n+1)]=1/n -1/(n+1)
1-1/2+1/2+1/3+……+1/99-1/100=99/100
