tìm x biết a/1/2.4+1/4.6+…+1/(2x-2).2x= 11/48 b/ 1/5.8+1/8.11+1/11.14+…+1/x.(x+3)=101/1540

tìm x biết
a/1/2.4+1/4.6+…+1/(2x-2).2x= 11/48
b/ 1/5.8+1/8.11+1/11.14+…+1/x.(x+3)=101/1540

0 bình luận về “tìm x biết a/1/2.4+1/4.6+…+1/(2x-2).2x= 11/48 b/ 1/5.8+1/8.11+1/11.14+…+1/x.(x+3)=101/1540”

  1. Đáp án + Giải thích các bước giải:

    `a//`

    `(1)/(2.4)+(1)/(4.6)+….+(1)/((2x-2).2x)=(11)/(48)` `(ĐK:x\ne{0;1})`

    `=>(2)/(2.4)+(2)/(4.6)+….+(2)/((2x-2).2x)=(11)/(48).2`

    `=>(1)/(2)-(1)/(4)+(1)/(4)-(1)/(6)+….+(1)/(2x-2)-(1)/(2x)=(11)/(24)`

    `=>(1)/(2)-(1)/(2x)=(11)/(24)`

    `=>(1)/(2x)=(1)/(24)`

    `=>2x=24`

    `=>x=12   (TM)`

    `b//`

    `(1)/(5.8)+(1)/(8.11)+(1)/(11.14)+….+(1)/(x.(x+3))=(101)/(1540)` `(ĐK:x\ne{0;-3})`

    `=>(3)/(5.8)+(3)/(8.11)+(3)/(11.14)+….+(3)/(x.(x+3))=(101)/(1540).3`

    `=>(1)/(5)-(1)/(8)+(1)/(8)-(1)/(11)+(1)/(11)-(1)/(14)+….+(1)/(x)-(1)/(x+3)=(303)/(1540)`

    `=>(1)/(5)-(1)/(x+3)=(303)/(1540)`

    `=>(1)/(x+3)=(1)/(308)`

    `=>x+3=308`

    `=>x=305   (TM)`

     

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  2. Đáp án:

    $a/$ `1/(2 . 4) + 1/(4 . 6) +…+ 1/( (2x – 2) 2x) = 11/48`

    `⇔ 1/2 [1/2 – 1/4 + 1/4 – 1/6 + … + 1/(2x – 2) – 1/(2x)] = 11/48`

    `⇔ 1/2 + (- 1/4 + 1/4 – 1/6 + … + 1/(2x – 2) ) – 1/(2x) = 11/48 : 1/2`

    `⇔ 1/2 – 1/(2x) = 11/24`

    `⇔ 1/(2x) = 1/24`

    `⇔ 24 = 2x`

    `⇔ x=12`

    Vậy `x = 12`

    $b/$ `1/(5 . 8) + 1/(8 . 11) + 1/(11 . 14) + … + 1/(x (x + 3) ) = 101/1540`

    `⇔ 1/3 [1/5 – 1/8 + 1/8 – 1/11 + 1/11 – 1/14 + .. + 1/x – 1/(x + 3)] = 101/1540`

    `⇔ 1/5 + (- 1/8 + 1/8 – 1/11 + 1/11 – 1/14 + .. + 1/x) – 1/(x + 3) = 101/1540 : 1/3`

    `⇔ 1/5 – 1/(x + 3) = 303/1540`

    `⇔ 1/(x + 3) = 1/308`

    `⇔ 308 = x + 3`

    `⇔ x = 305`

    Vậy `x = 305`

     

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