The law calculation of 1 / 12 + 1 / 20 + 1 / 30 + 1 / 42 + 1 / 56

The law calculation of 1 / 12 + 1 / 20 + 1 / 30 + 1 / 42 + 1 / 56

1/12+1/20+1/30+1/42+1/56
=1/(3×4)+1/(4×5)+1/(5×6)+1/(6×7)+1/(7×8)
=1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8
=1/3-1/8
=5/24