1*1/2+1/2*1/3+1/3*1/4+1/4*1/5+1/5*1/6+1/6*1/7=1-1/2+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