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1/1*2+1/2*3+1/3*4+......+1/2013*2014=?

直接套用公式n*1/(n+1)=1/n-1/(n+1),每项拆分后的后一项与下一项的前项消去了.如1/(1*2)+1/(2*3)=1-1/2+1/2-1/3=2/3.所以结果为1-1/2014=2013/2014

1/1*2+1/2*3+1/3*4······+1/2013*2014 =(1-1/2)+(1/2-1/3)+(1/3-1/4)+...........+(1/2013-1/2014) =1-1/2014 =2013/2014

1/1*2+1/2*3+1/3*4+……+1/2012*20131/1*2=1-1/21/2*3=1/2-1/31/3*4=1/3-1/4同理1/2012*2013=1/2012-1/20131/1*2+1/2*3+1/3*4+……+1/2012*2013=1-1/2+1/2-1/3+1/3-1/4+……+1/2011-1/2012+1/2012-1/2013=1-1/2013=2012/2013

1/2+1/2*1/3+1/3*1/4+......+1/2013*1/2012 =1/1-1/2+1/2-1/3+1/3-1/4+...+1/2012-1/2013 =1-1/2013 =2012/2013

1/2+1/2*1/3+1/3*1/4+......+1/2014*1/2015 =1-1/2+1/2-1/3+1/3-1/4+...+1/2014-1/2015 =1-1/2015 =2014/2015 请好评 ~在右上角点击【评价】,然后就可以选择【满意,问题已经完美解决】了。 如果你认可我的回答,敬请及时采纳, ~你的采纳是我...

=1-1/2+1/2-1/3+1/3-1/4+……+1/2013-1/2014 =1-1/2014 =2013/2014

(-1*1/2)+(-1/2*1/3)+(-1/3*1/4)......(-1/2012*1/2013) = -(1-1/2)-(1/2-1/3)-(1/3-1/4)......-(1/2012-1/...

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