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1*2/1+2*3/1+...+2013*2014/1

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

=[2×(1+2013)×2013÷2+2014]÷2014 =(2×2014×2013÷2+2014)÷2014 =(2014×2013+2014)÷2014 =2014×(2013+1)÷2014 =2014×2014÷2014 =2014

简单啊,1/1*2=1-1/2 1/2*3=1/2-1/3 以此类推 1-1/2+1/2-1/3+1/3-。。。。+1/2013-1/2014=1-1/2014=2013/2014

首先给你更正一下,你分子分母写反了,因为分数线/相当于除号,分数线/的右下角才是分母,如2/3是3分之2 解: (1/2015-1)×(1/2014-1)×(1/2013-1)…(1/3-1)×(1/2-1) =(-2014/2015)×(-2013/2014)×(-2012/2013)…(-2/3)×(-1/2) =1/20。

答: 第n项分数的分母=(1+2+3+...+n)=(n+1)n/2 第n项分数=2/[n(n+1)]=2/n-2/(n+1) 原式 =2*[1-1/2+1/2-1/3+.....+1/2013-1/2014] =2*(1-1/2014) =2013/1007

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

答: 设a=1/2+1/3+...+1/2014,b=1/2+1/3...+1/2013 (1/2+1/3+...+1/2014)(1+1/2+1/3...+1/2013)-(1+1/2+1/3+...+1/2014)(1/2+1/3+...+1/2013) =a(1+b)-(1+a)b =a+ab-b-ab =a-b =1/2014

您好: |1/2-1|+|1/3-1/2|+.....+|1/2014-1/2013| =1-1/2+1/2-1/3+。。。+1/2013-1/2014 =1-1/2014 =2013/2014 如果本题有什么不明白可以追问,如果满意请点击“好评”或“采纳为满意回答” 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,...

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