Bài 1: Tìm x biết: 2 $\frac{2}{1.3}$ + $\frac{2}{3.5}$ + $\frac{2}{5.7}$ +…+ $\frac{2}{x(x+2)}$= $\frac{2015}{2016}$

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1. `2/1.3 + 2/3.5 + 3/5.7 + …. + 2/(x(x+2)) = 2015/2016`

   `1/1 – 1/3 + 1/3 – 1/5 +…+ 1/x – 1/(x+2) = 2015/2016`

   `1/1 – 1/(x+2) = 2015/2016`

   `1/(x+2) = 1/1 – 2015/2016`

   `1/(x+2) = 1/2016`

   `=> x+2 =2016`

   `=> x= 2016-2`

   `=> x= 2014`

   Vậy `x= 2014` 

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2. Đáp án + Giải thích các bước giải:

   `2/1.3+2/3.5+2/5.7+…+2/(x(x+2))=2015/2016`
   

   `=>1-1/3+1/3-1/5+1/5-1/7+…+1/x-1/(x+2)=2015/2016`
   

   `=>1-1/(x+2)=2015/2016`
   

   `=>1/(x+2)=1-2015/2016`
   

   `=>1/(x+2)=2016/2016-2015/2016`
   

   `=>1/(x+2)=1/2016`
   

   `=>x+2=2016`
   

   `=>x=2016-2`
   

   `=>x=2014`
   

   Vậy `x=2014`

    

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