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2分之1加6分之1加12分之1加30分之1加42分之1加56分之1加72分之1加90分之1加110分之1等于多少要過程快

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chenglaaaaa

將各分數通分為1/2+1/6+1/12+1/30+1/42+1/56+1/72+1/90+1/110，觀察分母為連續自然數乘積形式，利用拆項法：1/(n(n+1))=1/n - 1/(n+1)，依次拆項后相消，最終結果為1 - 1/11 = 10/11。
pandongxue

1/6+1/12+1/20+1/30+1/42+1/56 =2/12+1/12+1/20+1/30+1/42+1/56 =1/4+1/20+1/30+1/42+1/56 =5/20+1/20+1/30+1/42+1/56 =3/10+1/30+1/42+1/56 =1/3+1/42+1/56 =5/14+1/56 =3/8 滿意請及時采納
dsdvybmtohfz

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
770512263

1/6+1/12+1/20+......+1/72
=1/2*3+1/3*4+1/4*5.....+1/8*9
=(1/2-1/3)+(1/3-1/4)+ ......+(1/8-1/9)
=1/2-1/9=7/18
lysafas

1/2+1/6+1/12+·········＋1/90+1/110
=1-1/2+1/2-1/3+1/3-1/4+········+1/9-1/10+1/10-1/11
=1-1/11
=10/11
idqfzbeiph

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) =1/2-1/8 =3/8請采納回答

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