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一加上六分之一减去十二分之一减去二十分之一减去三十分之一减去四十二分之一

等于八分之一

1-1/6-1/12-1/20-1/30-1/42-1/56-1/72-1/90=1-(1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90)=1-(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+1/9-1/10)=1-(1/2-1/10)=1-2/5=3/5祝学习进步

1/2-1/6-1/12-1/20-1/30-1/42=1/2-(1/6+1/12+1/20+1/30+1/42)=1/2-(1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7)=1/2-(1/2-1/7)=1/2-1/2+1/7=1/7

1/6-1/12-1/20-1/30-1/42-1/56=(1/2-1/3)-(1/3-1/4)-(1/4-1/5)-(1/5-1/6)-(1/6-1/7)-(1/7-1/8)=1/2-1/3-1/3+1/8=-1/24

1-1/2-1/6-1/12-1/20-1/30=1-(1/2+1/6+1/12+1/20+1/30)=1-(1/1*2+1/2*3+……+1/5*6)=1-(1-1/2+1/2-1/3+1/3-1/4+……+1/5-1/6)=1-(1-1/6)=5/6

1/2 - 1/6 - 1/12 - 1/20 - 1/30 - 1/42=(1 - 1/2)-(1/2 - 1/3)-(1/3 - 1/4)-(1/4 - 1/5)-(1/5 - 1/6)=1 - 1/2-1/2 + 1/3 - 1/3 + 1/4- 1/4 + 1/5 - 1/5 + 1/6=1 + 1/6=1又1/6

原式=1-1/2-1/6-1/12-1/20-1/30-1/42-1/56-1/72-1/90 =1-(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)-(1/8-1/9)-(1/9-1/10) 去括号后可约去很多 最后=1/10 (裂项法)望采纳哦亲(づ ̄3 ̄)づ~

179/4620

二分之一减六分之一减十二分之一减二十分之一减三十分之一减四十二分之一减五十六分之一-1/72-1/90=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)-(1/8-1/9)-(1/9-1/10)=1/2-1/2+1/3-1/3-+1/4-1/4+1/5-1/5+..+1/9-1/9+1/10=1/10

1/2-1/6-1/12-1/20-1*30-1/42-1/56-1/72-1/90=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)-(1/8-1/9)-(1/9-1/10)=1/10

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