=(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
=(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