应该是：1/1*2*3+1/2*3*4+…+1/98*99*100=?因为 1/[n（n+1)(n+2)]=1/2{1/[n(n+1)-1/[(n+1)(n+2)]}所以 原式=1/2(1/(1*2)-1/(2*3)+1/(2*3)-1/(3*4)+.+1/(98*99)-1/(99*100)=1/2(1/2-1/9900)=1/2*4949/9900=4949/19800...