题目内容：

2分之1加上6分之1机上12分之1加上20分之1加上30分之1加上42分之1加上56分之1用简
用简便方法计算

优质解答

1/2+1/6+1/12+1/20+1/30+1/42+1/56
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8
=1-1/8
=7/8

追问：

写详细下可不可以

追答：

可以，用分裂项数法 1/2+1/6+1/12+1/20+1/30+1/42+1/56 =1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+1/(6*7)+1/(7*8) =1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8 =1-1/8 =7/8