Rút gọn 1/30+1/42+1/56+1/72+‧‧‧‧‧‧+1/9900

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Rút gọn
1/30+1/42+1/56+1/72+‧‧‧‧‧‧+1/9900

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Margaret 3 tuần 2021-08-13T13:46:29+00:00 2 Answers 1 views 0

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    0
    2021-08-13T13:47:44+00:00

    Đáp án:

    `1/{30}+1/{42}+1/{56}+1/{72}+‧‧‧‧‧‧+1/{9900}`

    `=1/{5.6}+1/{6.7}+1/{7.8}+1/{8.9}+…+1/{99.100}`

    `=1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-…+1/{99}-1/{100}`

    `=1/5-1/{100}`

    `=19/{100}`

     

    0
    2021-08-13T13:47:45+00:00

    Đáp án:

    Ta có : 

    $\dfrac{1}{30}$  + $\dfrac{1}{42}$  + $\dfrac{1}{56}$  + …. + $\dfrac{1}{9900}$ 

    = $\dfrac{1}{5.6}$ + $\dfrac{1}{6.7}$ + $\dfrac{1}{7.8}$ + …. + $\dfrac{1}{99.100}$

    = $\dfrac{1}{5}$ – $\dfrac{1}{6}$ + $\dfrac{1}{6}$ – $\dfrac{1}{7}$ + …. + $\dfrac{1}{99}$ – $\dfrac{1}{100}$

    = $\dfrac{1}{5}$ – $\dfrac{1}{100}$

    = $\dfrac{19}{100}$

    Giải thích các bước giải:

     

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