1/(2*3)+1/(3*4)+1/(4*5)+...+1/(98*99)+1/(99*100)
=1/2-1/3+1/3-1/4+1/4-1/5+...+1/98-1/99+1/99-1/100
=1/2-1/100
=49/100为什么，me是小学生我看不懂1/2*3=1/6=1/2-1/31/3*4=1/12=1/3-1/4以此类推那么：1/(2*3)+1/(3*4)+1/(4*5)+...+1/(98*99)+1/(99*100)=1/2-1/3+1/3-1/4+1/4-1/5+...+1/98-1/99+1/99-1/100中间的各数会约掉，原式=1/2-1/100=50/100-1/100=49/100