So sánh A và B A=2016/20017+2017/2018+2018/2019 B=2016+2017+2018/2017+2018+2019

0 bình luận về “So sánh A và B A=2016/20017+2017/2018+2018/2019 B=2016+2017+2018/2017+2018+2019”

1. Đáp án:

    $A>B$

   Giải thích các bước giải:

    $A=\dfrac{2016}{2017}+\dfrac{2017}{2018}+\dfrac{2018}{2019}\\
   B=\dfrac{2016+2017+2018}{2017+2018+2019}\\
   =\dfrac{2016}{2017+2018+2019}+\dfrac{2017}{2017+2018+2019}+\dfrac{2018}{2017+2018+2019}$
   Do $2017<2017+2018+2019\Rightarrow \dfrac{1}{2017}>\dfrac{1}{2017+2018+2019}$
   $\Rightarrow \dfrac{2016}{2017}>\dfrac{2016}{2017+2018+2019}$
   Do $2018<2017+2018+2019\Rightarrow \dfrac{1}{2018}>\dfrac{1}{2017+2018+2019}$
   $\Rightarrow \dfrac{2017}{2018}>\dfrac{2017}{2017+2018+2019}$
   Do $2019<2017+2018+2019 \Rightarrow \dfrac{1}{2019}> \dfrac{1}{2017+2018+2019}$
   $\Rightarrow \dfrac{2018}{2019}>\dfrac{2018}{2017+2018+2019}\\
   \Rightarrow \dfrac{2016}{2017}+\dfrac{2017}{2018}+\dfrac{2018}{2019}>\dfrac{2016+2017+2018}{2017+2018+2019}\\ A>B$

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