已知1/6等于1/2减1/3，1/12等于1/3减1/4……1/6加1/12加1/20加……加1/

已知1\/6=1\/2-1\/3,1\/12=1\/3-1\/4,1\/20=1\/4-1\/5,那么1\/6+1\/12+1\/20+1\/...
根据1\/2-1\/3=1\/6,1\/3-1\/4=1\/12,1\/4-1\/5=1\/20…计算1\/6+1\/12+1\/20+1\/30+1\/42+1\/56+1\/72+1\/90的值。急！ ∵1\/2-1\/3=1\/6,1\/3-1\/4=1\/12,1\/4-1\/5=1\/20 ∴1\/5-1\/6=1\/30,1\/6-1\/7=1\/42,1\/7-1\/8=1\/56，1\/8-1\/9=1\/72,1\/9-1\/10=1\/90...

1\/6=1\/2-1\/3,1\/12=1\/3-1\/4,1\/20=1\/4-1\/5,根据以上规律计算下题。1\/...
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\/8-1\/9 =1\/2-1\/9 =9\/18-2\/18 =7\/18

1\/2=1-1\/2,1\/6=1\/2-1\/3,1\/12=1\/3-1\/4...请根据以上的规律计算:1\/6+1\/...
解：1\/6+1\/12+1\/20+1\/30+1\/42 =（1\/2-1\/3）+（1\/3-1\/4）+（1\/4-1\/5）+（1\/5-1\/6）+（1\/6-1\/7）=1\/2-1\/3+1\/3-1\/4+1\/4-1\/5+1\/5-1\/6+1\/6-1\/7 =1\/2-（1\/3-1\/3）-（1\/4-1\/4）-（1\/5-1\/5）-（1\/6-1\/6）-1\/7 =1\/2-0-0-0-0-1\/7...

数学题 1\/3+1\/6=1\/2 1\/4+1\/12=1\/3 1\/5+1\/20=1\/4 …… 1\/x+
回答：第四排是: 1\/6+1\/30=1\/5 ... 1\/81-1\/80 =-1\/6480

1\/2=1-1\/2,1\/6=1\/2-1\/3,1\/12=1\/3-1\/4
1\/2+1\/6+1\/12+1\/20+1\/30+1\/42+1\/56 =1-1\/2+1\/2-1\/3+1\/3-1\/4+...+1\/7-1\/8 =1-1\/8 =7\/8;如果本题有什么不明白可以追问，如果满意记得采纳 如果有其他问题请采纳本题后另发点击向我求助，答题不易，请谅解，谢谢。祝学习进步 ...

1\/6+1\/12+1\/20+1\/30+1\/42等于几
1\/6 可以写成 1\/2 - 1\/3，因为1\/2是3个单位的1\/6，1\/3是2个单位的1\/6，所以1\/6是1\/2中减去1\/3的一部分。同理，1\/12 = 1\/3 - 1\/4，1\/20 = 1\/4 - 1\/5，1\/30 = 1\/5 - 1\/6，1\/42 = 1\/6 - 1\/7。将这些分数相加，可以抵消掉大部分项，只留下1\/2和1\/7：= ...

1\/2=1-1\/2,1\/6=1\/2-1\/3,1\/12=1\/3-1\/4,⋯请根据上面算式中的规律,完成...
解 原式 =(1-1\/2)+(1\/2-1\/3)+……+(1\/7-1\/8)=1+(1\/2-1\/2)+(1\/3-1\/3)+……+(1\/7-1\/7)-1\/8 =1-1\/8 =7\/8

1\/2+1\/6+1\/12+1\/20……1\/1640思考过程?
此题用的是这个式子的分解，1\/[n(n+1)]=1\/n-1\/(n+1)，所以1\/6=1\/2-1\/3，1\/12=1\/3-1\/4……故1\/2+1\/6+1\/12+1\/20+……1\/1640=1-1\/2+1\/2-1\/3+1\/3-1\/4+1\/4-1\/5+……+1\/40-1\/41=1-1\/41=40\/41，这种方法叫裂项相消，高中学习数列求和时会用到的。

1\/6+1\/12+1\/20+…+1\/90=?
1\/6+1\/12+1\/20+…+1\/90 =1\/(2*3)+1\/(3*4)+1\/(4*5)+...+1\/(9*10)=1\/2-1\/3+1\/3-1\/4+1\/4-1\/5+...+1\/9-1\/10 =1\/2-1\/10 =2\/5

1\/2+1\/6+1\/12+1\/20+1\/30+1\/42+1\/56+1\/72+1\/90+...1\/9900
裂项法 原式=1-1\/2+1\/2-1\/3+1\/3-1\/4+...+1\/99-1\/100 =1-1\/100 =99\/100