1/(1×2)+1/(2×3)+1/(3×4)+...+1/(98×99)+1/(99×100)
=1-1/2+1/2-1/3+1/3-1/4+...+1/98-1/99+1/99-1/100
=1- 1/100
=99/100
一般的,对于正整数n,1/[n(n+1)]=1/n -1/(n+1)