1/2+5/6-7/12+9/20-11/30+13/42-15/56
=1/2+(1/2+1/3)-(1/3+1/4)+(1/4+1/5)-(1/5+1/6)+(1/6+1/7)-(1/7+1/8)
=1/2+1/2-1/8
=7/8