六分之一+十二分之一+二十分之一+三十分之一+四十二分之一
=1/(2×3)+1/(3×4)+1/(4×5)+1/(5×6)+1/(6×7)
=1/2-1/3+1/3-1/4+1/4-1/5-1/5-1/6+1/6-1/7
=1/2-1/7
=3/7
六分之一+十二分之一+二十分之一+三十分之一+四十二分之一
=1/(2×3)+1/(3×4)+1/(4×5)+1/(5×6)+1/(6×7)
=1/2-1/3+1/3-1/4+1/4-1/5-1/5-1/6+1/6-1/7
=1/2-1/7
=3/7