Tìm x biết: 1/3+1/6=1/10+…..+2/x(x+1)=2016/2017

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1. Đáp án:

   1/3+1/6+1/10+…..+2/x(x+1)=2016/2017

   1/2.[1/3+1/6+1/10+…..+2/x(x+1)]=1/2.2016/2017

   1/6.1/12+1/20+………………..1/x.(x+1)=1008/2017

   1/2.3+1/3.4+1/4.5+………..+1/x-1/x-1=1008/2017

   1/2-1/3+1/3-1/4+………….+1/x-1/x-1=1008/2017

   1/2-(1/3-1/3)-…………………………..-(1/x-1/x)-1/x-1=1008/2017

   1/2-0-.-………..-0-1/x-1=1008/2017

   1/2-1/x-1=1008/2017

   2017/5034-1/x-1=2016/5034

   1/x-1=2017/5034-2016/5034

   1/x-1=1/5034

   =>x-1=5034

     x=5034+1=5035

   Vậy x=5035

   Cho mình xin hay nhất về cho nhóm ạ

   Thank you very much

    

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2. `1/3+1/6+1/10+…..+2/(x(x+1))=2016/2017`

   `=> 2/6 + 2/12 + 2/20 + ….. + 2/(x(x+1))=2016/2017`

   `=> 2/(2.3) + 2/(3.4) + 2/(4.5) + ….. + 2/(x(x+1))=2016/2017`

   `=> 2(1/(2.3) + 1/(3.4) + 1/(4.5) + ….. + 1/(x(x+1)))=2016/2017`

   `=> 2(1/2 – 1/3 + 1/3 – 1/4 + 1/4- 1/5 + ….. + 1/x – 1/(x+1))=2016/2017`

   `=> 2(1/2 – 1/(x+1)) =2016/2017`

   `=> 1/2 – 1/(x+1) = 1008/2017`

   `=> 1/(x+1) = 1/4034`

   `=> 1.4034 = 1(x+1) `

   `=> 4034 = x+1`

   `=> x = 4033`

   (Ăn tết ngon miệng ạ)

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