所以1/2+1/6+1/12+1/20+1/30+1/42=1/2+1/2-1/7=6/7
6/7+1/26=163/182
另外我觉得你可能题抄错了，1/26目测是1/56=1/7-1/8
这样最后答案就是1/2+1/2-1/8=7/8
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;
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1-1/8=7/8.
...请根据以上的规律计算:1\/6+1\/12+1\/20+1\/30+1\/42
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...
...根据上述规律计算下题:1\/2+1\/6+1\/12+1\/20+1\/30=
原式=（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 =5\/6
1-1\/2=1\/2,1\/2-1\/3=1\/6,1\/3-1\/4=1\/12,1\/4-1\/5=1\/20,你发现了什么?
我发现当减数与被减数分子均为一时，结果的分母等于减数与被减数分母的积，分子为一
计算: 1÷(1\/2+1\/6+1\/12+1\/20...+1\/342+1\/380)=?
1\/6=1\/2-1\/3 1\/12=1\/3-1\/4 ……1\/342=1\/18-1\/19 1\/380=1\/19-1\/20 这些相加就是1-1\/20=19\/20 所以答案是20\/19
1\/2+1\/6+1\/12+1\/20+1\/30+1\/42的简便运算?
1\/6，1\/12这三个数分母通分都为12。1\/20，1\/30分母通分为60。所以，简便运算先算前三个数和最后一个数。原=1\/2+1\/6+1\/12+1\/42+1\/20+1\/30 =6\/12+2\/12+1\/12+1\/42+3\/60+2\/60 =9\/12+1\/42+5\/60 =9\/12+1\/42+1\/12 =10\/12+1\/42 =70\/84+2\/84 =72\/84 =6\/7 ...
求1\/2+1\/6+1\/12+1\/20...+1\/2450的计算答案,要具体算式。谢谢!
因为 1\/2=1-1\/2 1\/6=1\/2-1\/3 1\/12=1\/3-1\/4 ...1\/2450=1\/49-1\/50 所以原式=1-1\/2+1\/2-1\/3...+1\/49-1\/50 =1-1\/50=49\/50
...1\/2= 1\/2-1\/3= 1\/3-1\/4= 算出得数,想一想,你发现了什么?
因为[n(n+1)]分之1=n分之1-(n+1)分之1 所以1\/2+1\/6+1\/12+1\/20=5分之4
简便计算1\/2+1\/6+1\/12+1\/20+1\/30+1\/42?
12、20、30、42分解为2×3、3×4、4×5、5×6、6×7，然后再化简。1\/2+1\/6+1\/12+1\/20+1\/30+1\/42 =1\/2+1\/（2×3）+1\/（3×4）+1\/（5×6）+1\/（6×7）=1\/2+（1\/2-1\/3）+（1\/3-1\/4）+（1\/5-1\/6）+（1\/6-1\/7）=1\/2+1\/2-1\/7 =1-1\/7 =6\/7 ...
1\/2+1\/6+1\/12+1\/20+1\/30+1\/42+1\/?
所以可得：1\/2+1\/6+1\/12+1\/20+1\/30+1\/42+1\/56+1\/72+1\/90 =1\/(1*2)+1\/(2*3)+1\/(3*4)+1\/(4*5)+1\/(5*6)+1\/(6*7)+1\/(7*8)+1\/(8*9)+1\/(9*10)=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 ...
1\/2+1\/6+1\/12+1\/20+1\/30+1\/42怎么算
1\/2+1\/6+1\/12+1\/20+1\/30+1\/42 =1\/(1x2)+1\/(2x3)+1\/(3x4)+1\/(4x5)+1\/(5x6)+1\/(6x7)=(1 -1\/2) +(1\/2-1\/3)+...+(1\/6-1\/7)=1 -1\/7 =6\/7
