1/6+1/12+1/20+1/30+1/42+1/56+1/72等于多少?

最小共约分母2520
1/6+1/12+1/20+1/30+1/42+1/56+1/72
=(420+210+126+84+60+45+35）/2520
=980/2520
=7/18

1/6+1/12+1/20+1/30+1/42+1/56+1/72
=(1/6+1/12)+(1/20+1/30)+1/42+1/56+1/72
=3/12+1/12+1/42+1/56+1/72
=1/3+1/42+1/56+1/72
=(1/3+1/42)+1/56+1/72
=5/14+1/56+1/72
=3/8+1/72
=7/18

1/6+1/12+1/20+1/30+1/42+1/56+1/72
=1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8+1/8*9
=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9
=1/2-1/9
=7/18

1/6+1/12+1/20+1/30+1/42+1/56+1/72
=1/(2x3)+1/(3x4)+..+1/(8x9)
=(1/2-1/3)+(1/3-1/4)+..+(1/8-1/9)
=1/2-1/9
=7/18

1/6+1/12+1/20+1/30+1/42+1/56+1/72
＝1／2－1／3＋1／3－1／4＋1／4＋1／5－1／5－1／6＋1／6－1／7＋1／7－1／8＋1／8－1／9
＝1／2－1／9
＝7／18

用裂项法：
=1／2-1／9
=7／18

1/6+1/12+1/20+1/30+1/42+1/56+1/721/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8+1/8*9=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9=1/2-1/9=(9-2)/18=7/18

1/6+1/12+1/20+1/30+1/42+1/56+1/72

=(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+(1/7-1/8)+(1/8-1/9)
=1/2-1/9
=7/18