12分之一+20分之一+30分之一+36分之一+42分之一= (要简便方法)

1/12+1/20+1/30+1/36+1/42
=1/3*4+1/4*5+1/5*6+1/6*7+1/36
=1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/36
=1/3-1/7+1/36
=4/21+1/36
=55/252

原式=1/3*4+1/4*5+1/5*6+1/6*7
=1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7
=1/3-1/7
=4/21

原式=
=1/(3*4)+1/(4*5)+1/(5*6)+1/(6*7)
=1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7
=1/3-1/7
=4/21

1/12+1/20+1/30+1/36+1/42
=1/3*4+1/4*5+1/5*6+1/6*7+1/36
=（1/3-1/7）*1+1/36
=4/21*1+1/36
=55/252

12分之一等于3分之一减去4分之一，20分之一等于4分之一减去5分之一。。。。42分之一等于6分之一减去7分之一最后结果是3分之一减去7分之一！

1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7=4/21