1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90
=1/2×3+1/3×4+1/4×5+1/5×6+1/6×7+1/7×8+1/8×9+1/9×10
=(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+(1/7-1/8)+(1/8-1/9)+(1/9-1/10)
=1/2-1/10
=2/5