So sánh `2018/2019+2019/2020+2020/2021+2021/2018` với `4`

So sánh
`2018/2019+2019/2020+2020/2021+2021/2018` với `4`

0 bình luận về “So sánh `2018/2019+2019/2020+2020/2021+2021/2018` với `4`”

  1. Đáp án:

    $\dfrac{2018}{2019} + \dfrac{2019}{2020} + \dfrac{2020}{2021} +\dfrac{2021}{2018} > 4$

    Giải thích các bước giải:

    Ta có:

    $\dfrac{2018}{2019} + \dfrac{2019}{2020} + \dfrac{2020}{2021} +\dfrac{2021}{2018} – 4$

    $= \left(\dfrac{2018}{2019} -1\right) + \left(\dfrac{2019}{2020} -1\right)+\left(\dfrac{2020}{2021} -1\right)+\left(\dfrac{2021}{2018} -1\right)$

    $= -\dfrac{1}{2019} -\dfrac{1}{2020} -\dfrac{1}{2021} +\dfrac{3}{2018}$

    $= \left(\dfrac{1}{2018} -\dfrac{1}{2019}\right)+ \left(\dfrac{1}{2018} -\dfrac{1}{2020}\right)+\left(\dfrac{1}{2018} -\dfrac{1}{2021}\right) > 0$

    Do đó:

    $\dfrac{2018}{2019} + \dfrac{2019}{2020} + \dfrac{2020}{2021} +\dfrac{2021}{2018} > 4$

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