x/1*2+x/2*3+x/3*4+…+x/2009*2010=2009

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/25 15:49:14
x/1*2+x/2*3+x/3*4+…+x/2009*2010=2009
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x/1*2+x/2*3+x/3*4+…+x/2009*2010=2009
x/1*2+x/2*3+x/3*4+…+x/2009*2010=2009

x/1*2+x/2*3+x/3*4+…+x/2009*2010=2009
用裂项法
原式可化为
x(1-1/2+1/2-1/3+...+1/2009-1/2010)=2009
x*2009/2010=2009
x=2010

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