tìm x biết rằng $\frac{1}{10}$+ $\frac{1}{15}$ + $\frac{1}{21}$ +…+ $\frac{2}{x(x+1)}$ = $\frac{2010}{2012}$

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1. `1/10 + 1/15 + 1/21 +…+ 2/(x(x+1)) = 2010/2012`

   `1/2 ( 1/10 + 1/15 + 1/21+…+ 2/(x(x+1)) = 2010/2012 . 1/2`

   ` 1/20 + 1/30 + 1/42 + …+ 1/(x(x+1) = 1005/2012`

   `1/4.5 + 1/5.6 + 1/6.7 +…+ 1/x – 1/(x+1) = 1005/2012`

   `1/4 – 1/5 + 1/5 – 1/6 + 1/6 – 1/7+…+1/x – 1/(x+1) = 1005/2012`

   `1/4 – 1/(x+1) = 1005/2012`

   `1/(x+1) = 1/4 – 1005/2012`

   `1/(x+1) =-251/1006`

   `-251(x+1) = 1006`

   `-251x – 251 = 1006`

   `-251x =1257`

   `x= 1257 : (-251)`

   `x= -1257/251`

   Vậy `x= -1257/251`

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