tìm x `1/3 + 1/6 + 1/10 + ….. + 2/(x (x + 1) ) = 2013/2015`

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1. `1/3+1/6+1/10+…+2/(x(x+1)) =2013/2015`

   `1/3+1/6+1/10+…+1/(x(x+1):2) =2013/2015`

   `2/6+2/12+2/20+…+2/(x(x+1))=2013/2015`

   `2(1/2.3+1/3.4+1/4.5+…+1/(x(x+1)))=2013/2015`

   `2(1/2-1/3+1/3-1/4+1/4-1/5+…+1/x-1/(x+1))=2013/2015`

   `2(1/2-1/(x+1))=2013/2015`

   `1/2-1/(x+1)=2013/2015:2`

   `1/2-1/(x+1)=2013/4030`

   `1/(x+1)=1/2-2013/4030`

   `1/(x+1)=1/2015`

   `x+1=2015`

   `x=2015-1`

   `x=2014`

   Vậy `x=2014`.

    

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2. `1/3 + 1/6 + 1/10 + … + 2/(x(x + 1)) =2013/2015`

   `⇔2/6 +2/12 + 2/20 + … + 2/(x(x + 1)) =2013/2015`

   `⇔2/2.3 + 2/3.4 + 2/4.5 + … +2/(x(x + 1)) =2013/2015`

   `⇔2.(1/2.3 + 1/3.4 + … +1/(x (x+1))) = 2013/2015`

   `⇔ 2.(1/2 – 1/3 + 1/3 – 1/4 + … + 1/x – 1/(x + 1)) = 2013/2015`

   `⇔2(1/2 – 1/(x + 1)) = 2013/2015`

   `⇔1/2 – 1/(x + 1) = 2013/2015 : 2`

   `⇔1/2 – 1/(x + 1) = 2013/4030`

   `⇔ 1/(x + 1) = 1/2 – 2013/4030`

   `⇔1/(x + 1) =2015/4030 – 2013/4030`

   `⇔ 1/(x + 1) = 1/1015`

   `⇔  x + 1 . 1 = 1 . 1015`

   `⇔x + 1 = 1015`

   `⇔x = 2015 – 1`

   `⇔x  =2014`

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