tìm x 1/28 + 1/36 + 1/45 + …+ 2/ x.(x + 1) = 4/15 (-9)/x = x ²/3

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1. Tham khảo

    `a) \frac{1}{28}+\frac{1}{36}+…+\frac{2}{x(x+1)}=\frac{4}{15}`

   `⇒\frac{2}{56}+\frac{2}{72}+…+\frac{2}{x(x+1)}=\frac{4}{15}`

   `⇒\frac{2}{7.8}+\frac{2}{8.9}+…+\frac{2}{x(x+1)}=\frac{4}{15}`

   `⇒2.(\frac{1}{7.8}+\frac{1}{8.9}+…+\frac{1}{x(x+1)})=\frac{4}{15}`

   Áp dụng `\frac{1}{n(n+1)}=\frac{1}{n}-\frac{1}{n+1}(n \ne 0,-1)`

   `⇒\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+..+\frac{1}{x}-\frac{1}{x+1}=\frac{2}{15}`

   `⇒\frac{1}{7}-\frac{1}{x+1}=\frac{2}{15}`

   `⇒\frac{1}{x+1}=\frac{1}{105}`

   `⇔x+1=105`

   `⇒x=104`

   Vậy `x=104`

   `b) \frac{-9}{x}=\frac{x^2}{3}(x \ne 0)`

   `⇒x.x^2=-9.3`

   `⇒x^3=-27`

   `⇒x^3=(-3)^3`

   `⇒x=-3`

   Vậy `x=-3`

   `\text{©CBT}`

    

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2. Đáp án:

   `@` 

   `1/28 + 1/36 + 1/45 + … + 2/ (x.(x + 1)) = 4/15`

   `->  2/56+ 2/72+2/90 + …. + 2/ (x.(x + 1)) = 4/15`

   `-> 2/(7.8) + 2/(8.9) + 2/(9.10) + …. + 2/(x.(x + 1)) = 4/15`

   `-> 2.(1/(7.8) + 1/(8.9) + 1/(9.10) + …. + 1/(x.(x + 1))) = 4/15`

   `-> 1/(7.8) + 1/(8.9) + 1/(9.10) + …. + 1/(x.(x + 1)) = 4/15 : 2 = 2/15`

   `-> 1/7 – 1/8 + 1/8 – 1/9 + … + 1/x – 1/x+1 = 2/15`

   `-> 1/7 – 1/(x+1) = 2/15`

   `-> 1/x+1 = 2/105`

   `-> x+1 = 105`

   `-> x = 104`

   Vậy `x = 104`

   `@`

   `(-9)/x = x ²/3`

   `-> x.x^2 = (-9) . 3`

   `-> x^3 = -27`

   `-> x = -3`

   Vậy `x = -3`

   `Go od luck!` 

    

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