Tính nhanh : `C = 1/2+1/14+1/35+1/65+1/104+1/152`

Tính nhanh : `C = 1/2+1/14+1/35+1/65+1/104+1/152`

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  1. Đáp án:

    `C = 1/2 + 1/14 + 1/35 + 1/65 + 1/104 + 1/152`

    `-> C = 2/4 + 2/28 + 2/70 + 2/130 + 2/208 + 2/304`

    `-> C = 2/(1 . 4) + 2/(4 . 7) + 2/(7 . 10) + 2/(10 . 13) + 2/(13 . 16) + 2/(16 . 19)`

    `-> C = 2 . [1/(1 . 4) + 1/(4 . 7) + 1/(7 . 10) + 1/(10 . 13) + 1/(13 . 16) + 1/(16 . 19)]`

    `-> C = 2 . 1/3 [1 – 1/4 + 1/4 – 1/7 + 1/7 – 1/10 + 1/0 – 1/13 + 1/13 – 1/16 + 1/16 – 1/19]`

    `-> C = 2/3 . [1 + (- 1/4 + 1/4 – 1/7 + 1/7 – 1/10 + 1/0 – 1/13 + 1/13 – 1/16 + 1/16) – 1/19]`

    `-> C = 2/3 . [1 – 1/19]`

    `-> C = 2/3 . 18/19`

    `-> C =12/19`

    Vậy `C = 12/19`

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  2. Đáp án:

     

    Giải thích các bước giải:

    `C = 1/2+1/14+1/35+1/65+1/104+1/152`

    $=\dfrac{2}{4}+\dfrac{2}{28}+\dfrac{2}{70}+\dfrac{2}{130}+\dfrac{2}{208}+\dfrac{2}{304}$

    $=\dfrac{2}{3}\cdot(\dfrac{3}{4}+\dfrac{3}{28}+\dfrac{3}{70}+\dfrac{3}{130}+\dfrac{3}{208}+\dfrac{3}{304})$

    $=\dfrac{2}{3}\cdot(\dfrac{3}{1\cdot4}+\dfrac{3}{4\cdot7}+\dfrac{3}{7\cdot10}+\dfrac{3}{10\cdot13}+\dfrac{3}{13\cdot16}+\dfrac{3}{16\cdot19})$

    $=\dfrac{2}{3}\cdot(\dfrac{1}{1}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{19})$

    $=\dfrac{2}{3}\cdot(1-\dfrac{1}{19})$

    $=\dfrac{2}{3}\cdot\dfrac{18}{19}$

    $=\dfrac{12}{19}$

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