1/12+1/20+1/30+1/42=?简便计算,

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

1/12+1/20+1/30+1/42
=( 1/20+1/30) +( 1/12 +1/42)
= (3+2)/60 + ( 7+2) /84
= 1/ 12 + 3/28
= ( 7+ 9) /84
= 16/84
= 4/ 21

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