1+1/2+1/6+1/12+1/20+1/30+1/42
=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+1-1/7
=2-1/7
=13/7