1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72=简便计算,有算式,要简便

Question

1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72= 简便计算,
有算式,要简便

Answer 1

1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72
=1/(1*2)+1/(2*3)+1/(3*4)+...+1/(8*9)
=1-1/2+1/2-1/3+...+1/8-1/9
=1-1/9
=8/9