So sánh : `C=1/4+frac\{1}{4^2}+frac{1}{4^3}+…+frac{1}{4^100}` với `1/3`

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So sánh : `C=1/4+frac\{1}{4^2}+frac{1}{4^3}+…+frac{1}{4^100}` với `1/3`

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Genesis 5 tháng 2021-07-17T19:15:01+00:00 2 Answers 4 views 0

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    0
    2021-07-17T19:16:01+00:00

    `C=1/4+1/4^2+1/4^3+…+1/4^100`

    `⇒4C=1+1/4+1/4^2+…+1/4^99`

    `⇒4C-C=(1+1/4+1/4^2+…+1/4^99)-(1/4+1/4^2+1/4^3+…+1/4^100)`

    `⇒3C=1-1/4^100`

    `⇒C=(1-1/4^100)/3`

    `\text{Vì}` `1-1/4^100<1` `\text{nên}` `(1-1/4^100)/3<1/3`.

    `\text{Vậy}` `C<1/3`.

    0
    2021-07-17T19:17:00+00:00

    Ta có : 

    `4C=1+1/4+frac\{1}{4^2}+frac\{1}{4^3}+…+1/99`

       `C=1/4+frac\{1}{4^2}+frac\{1}{4^3}+…+frac\{1}{4^99}+frac\{1}{4^100}`

    `=>4C-C=1-frac\{1}{4^100}`

    `=>3C=1-frac{1}{4^100}<1`

    `=>3C<1`

    `=>C<1/3`

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