∵1/1*2*3-1/2*3*4=(4-1)/1*2*3*4=3/1*2*3*4,∴1/1*2*3*4=(1/3)*(1/1*2*3-1/2*3*4)同理1/2*3*4*5=(1/3)*(1/2*3*4-1/3*4*5).1/97*98*99*100=(1/3)*(1/97*98*99-1/98*99*100)∴原式=(1/3)*(1/1*2*3-1/98*99*100)=1/3(1...