1/2+1/6+1/12+1/20+1/30+1/42+1/56
=(1/1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+(1/7-1/8)
=1/1+(-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+0+0+0+0+0+0-1/8
=1-1/8
=7/8