(1/2+1/3+1/4+…+1/2012+1/2013).x=2012/1+2011/2+2010/3+…+2/2011+1/2012

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1. Đáp án:

   `↓↓` 

   Giải thích các bước giải:

   `(1/2+1/3+1/4+…+1/2012+1/2013).x=2012/1+2011/2+2010/3+…+2/2011+1/2012`

   `=> x=( 2012/1+2011/2+2010/3+…+2/2011+1/2012 ):(1/2+1/3+1/4+…+1/2012+1/2013)`

   Gọi `A=( 2012/1+2011/2+2010/3+…+2/2011+1/2012 ):(1/2+1/3+1/4+…+1/2012+1/2013)`

   `A=(2012/1+2011/2+2010/3+…+2/2011+1/2012)/(1/2+1/3+1/4+…+1/2012+1/2013)`

   `=(2012/1+1+2011/2+1+2010/3+1+…+2/2011+1+1/2012+1)/(1/2+1/3+1/4+…+1/2012+1/2013)`

   `=(1+2013/2+2013/3+….+2013/2012)/(1/2+1/3+1/4+…+1/2012+1/2013)`

   `=(2013.(1/2+1/3+….+1/2012+1/2013))/(1/2+1/3+1/4+…+1/2012+1/2013)`

   `=2013`

   `=> x=2013`

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