rút gọn 2019^2020 -2019^2019 +2019^2018 – 2019^2017+ … +2019^2 -2019

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1. Đáp án:

   $\begin{array}{l}
   A = {2019^{2020}} – {2019^{2019}} + {2019^{2018}} – …\\
    + {2019^2} – 2019\\
    \Rightarrow 2019.A = {2019^{2021}} – {2019^{2020}} + {2019^{2019}} – …\\
    + {2019^3} – {2019^2}\\
    \Rightarrow A + 2019A = {2019^{2021}} – 2019\\
    \Rightarrow 2020.A = {2019^{2021}} – 2019\\
    \Rightarrow A = \dfrac{{{{2019}^{2021}} – 2019}}{{2020}}
   \end{array}$

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