因为1/2=1/1x1/2=1-1/2,1/6=1/2x1/3=1/2-1/3, 以此类推,1/42=1/6-1/7, 则原式=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7 =1-1/7 =6/7.