1/(1*2*3)+1/(2*3*4)+1/(3*4*5)+…+1/(98*99*100)
=(1-1/2-1/3)+(1/2-1/3-1/4)+(1/3-1/4-1/5)+.1/98-1/99-1/100
=1-1/100
=99/100
备注：1/(1*2*3)=1-1/2-1/3
祝国庆节快乐!