tìm x ∈n:1/21+1/28+1/36+…+2/x(x+1)=2/9

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1. `1/21+1/28+1/36+…+2/(x(x+1))=2/9`

   `to 1/3.7 + 1/4.7 + 1/4.9 + … +2/(x(x+1))=2/9`

   `to 2/6.7 + 2/8.7 + 2/8.9 + … + 2/(x(x+1)) = 2/9`

   `to 2 . (1/6.7 + 1/7.8 + 1/8.9 + … + 1/(x(x+1)) ) = 2/9`

   `to 1/6-1/7+1/7-1/8+1/8-1/9+…+1/x-1/(x+1)=1/9`

   `to 1/6-1/(x+1)=1/9`

   `to 1/(x+1)=1/18`

   `to x+1=18`

   `to x=17`

   Vậy `x=17`

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2. Đáp án:

    

   Giải thích các bước giải:

    `1/21+ 1/28+ 1/36+…+ 2/(x. (x+ 1))= 2/9`

   `2/42+ 2/56+ 2/72+…+ 2/(x. (x+ 1))= 2/9`

   `2. (1/42+ 1/56+ 1/72+…+ 1/(x. (x+ 1)))= 2/9`

   `(1/(6. 7)+ 1/(7. 8)+ 1/(8. 9)+…+ 1/(x. (x+ 1)))= 2/9: 2`

   `(1/6- 1/7+ 1/7- 1/8+ 1/8- 1/9+…+ 1/x- 1/(x+ 1))= 1/9`

   `1/6- 1/(x+ 1)= 1/9`

   `1/(x+ 1)= 1/6- 1/9`

   `1/(x+ 1)= 3/18- 2/18`

   `1/(x+ 1)= 1/18`

   `⇒ x+ 1= 18`

   `x= 18- 1`

   `x= 17`

   Vậy `x= 17`

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