1/3+1/3^2+1/3^3+1/3^4+…+1/3^99+1/3^100

1/3+1/3^2+1/3^3+1/3^4+…+1/3^99+1/3^100

0 bình luận về “1/3+1/3^2+1/3^3+1/3^4+…+1/3^99+1/3^100”

  1. Đặt `A = 1/3+1/3^2+1/3^3+1/3^4+…+1/3^99+1/3^100`

    `=> 3A =1 + 1/3+1/3^2+1/3^3+1/3^4+…+1/3^99+1/3^99`

    `=> 3A – A = (1 + 1/3+1/3^2+1/3^3+1/3^4+…+1/3^99+1/3^99) –   (1/3+1/3^2+1/3^3+1/3^4+…+1/3^99+1/3^100)`

    `=> 2A = 1 – 1/3^100`

    `=> A = (1- 1/3^100)/2`

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  2. Đáp án + Giải thích các bước giải:

    Đặt `A=1/3+1/3^2+1/3^3+…+1/3^100`

    `=>3A=1+1/3+1/3^2+…+1/3^99`

    `=>3A-A=(1+1/3+1/3^2+…+1/3^99)-(1/3+1/3^2+1/3^3+…+1/3^100)`

    `=>2A=1-1/3^100`

    `=>A=(1-1/3^100)/2`

     

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