cho S = 1/5 mũ 2+ 1/6 mũ 2+……..+1/2020 mũ 2

Question

cho S = 1/5 mũ 2+ 1/6 mũ 2+……..+1/2020 mũ 2

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Cora 3 tuần 2021-11-21T17:15:16+00:00 2 Answers 3 views 0

Answers ( )

    0
    2021-11-21T17:16:27+00:00

    Ta có:

    ` 1/5^2 < \frac{1}{4.5} `

    ` 1/6^2 < \frac{1}{5.6} `

    ` ……. `

    ` 1/2020^2 < \frac{1}{2019.2020} `

    ` => 1/5^2 + 1/6^2 + … + 1/2020^2 < \frac{1}{4.5} + \frac{1}{5.6} + … + \frac{1}{2019.2020} `

    ` => S < \frac{1}{4.5} + \frac{1}{5.6} + … + \frac{1}{2019.2020} `

    ` => S < 1/4 – 1/5 + 1/5 – 1/6 + … + 1/2019 . 1/2020 `

    ` => S < 1/4 – 1/2020 `

    Do: ` 1/4 – 1/2020 < 1/4 `

    ` => S < 1/4 ` (1)

    Ta có:

    ` 1/5^2 > \frac{1}{5.6} `

    ` 1/6^2 > \frac{1}{6.7} `

    ` ……….. `

    ` 1/2020^2 > \frac{1}{2020.2021} `

    ` => 1/5^2 + 1/6^2 + … + 1/2020^2 > \frac{1}{5.6} + \frac{1}{6.7} + … + \frac{1}{2020.2021} `

    ` => S > \frac{1}{5.6} + \frac{1}{6.7} + … + \frac{1}{2020.2021} `

    ` => S > 1/5 – 1/6 + 1/6 – 1/7 + … + 1/2020 – 1/2021 `

    ` => S > 1/5 – 1/2021 `

    Do: ` 1/5 – 2021 > 1/6 `

    ` => S > 1/6 ` (2) 

    Từ (1) và (2):

    ` => 1/6 < S < 1/4 ` ` (đpcm) `

    0
    2021-11-21T17:17:10+00:00

    Cách làm

    ta thấy

    1/5^2<1/4.5

    1/6^2<1/5.6

    ……………………

    1/2020^2<1/2019.2020

    => 1/5^2+1/6^2+…+1/2020^2<1/4.5+1/5.6+1/2019.2020

    =1/4-1/5+1/5-1/6+…+1/2019-1/2020

    =1/4-1/2020

    lại có

    1/5^2>1/5.6

    1/6^2>1/6.7

    …………………….

    1/2020^2>1/2020.2021

    mk dang bận nên chỉ làm đc đến đây thôi chúc bạn học tốt

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