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1X1/2+1/2X1/3+1/3X1/4+1/4X1/5+1/5X1/6+1/6X1/7,...

原式=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)+(1/6-1/7) =1-1/7 =6/7 公式: 1/a乘1/(a+1)=1/a-1/(a+1)其中a是正整数

1x1/2+1/2x1/3+1/3x1/4+1/4x1/5+1/5x1/6+1/6x1/7 =1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/9-1/7 =1-1/7 =6/7

利用裂项相消法:1/nx1/(n+1)=1/n-1/(n+1) (-1x1/2)+(-1/2x1/3)+(-1/3x1/4)+…+(-1/2015x1/2016) =-[(1x1/2)+(1/2x1/3)+(1/3x1/4)+…+(1/2015x1/2016)] =-(1-1/2+1/2-1/3+1/3-1/4+,,,,,,,+1/2015-1/2016) =-(1-1/2016) =-2015/2016

解: 原式=-(1-1/2+1/2-1/3+1/3-1/4+...+1/2012-1/2013) =-(1-1/2013) =-2012/2013

=1/2+2/3+3/4+4/5+5/6+6/7+7/8……+2004/2005 =(1-1/2)+(1-1/3)+(1-1/4)+(1-1/5)……(1-1/2005) =2004-(1/2+1/3+1/4+1/5+1/6+1/7+1/8……1/2005) 1/2+1/3+…+1/n是没有好的计算公式的,所有计算公式都是计算近似值的,且精确度不高。 1/2+1/3+1/4+1/5...

你第三个是不是3*1/4啊? 如果是我们可以把这个式看成 (1-1/2)+(1-1/3)+……+(1-1/100) =1×100-(1/2+1/3+……1/100) =100-(5049/200)【首项加末项乘以项数除以2】 =14951/200

你化错了. 应该是 1 0 0 1 0 1 0 2 0 0 1 1 0 0 0 0

因为1X1=1,表达的含义是一个1,结果是1;同理,表达的含义是两个2,结果是4。而1+1=2,意思可以用具体的事代入,比如1个苹果加上1个苹果,不就总共2个苹果了吗?2+2=4,也是同样的道理。

(-1x1/2)+(-1/2x1/3)+(-1/3x1/4)+……+(-1/2013x1/2014) =-(1x1/2)-(1/2x1/3)-(1/3x1/4)-……-(1/2013x1/2014) =-[(1x1/2)+(1/2x1/3)+(1/3x1/4)+……+(1/2013x1/2014)] =-[(1-1/2)+(1/2-1/3)+(1/3-1/4)+……+...

=2x(1-1/3+1/3-1/5+……+1/47-1/49) =2x(1-1/49) =96/49

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