a, D= 1+2+2^2+2^3+……+2^2020 cho D+1 là một lũy thừa b, E=2^100-2^99+2^98-2^97+…….2^2-2+1 F=3^2020-3^2019+3^2018-3^2017+…..+3^2-3+1

0 bình luận về “a, D= 1+2+2^2+2^3+……+2^2020 cho D+1 là một lũy thừa b, E=2^100-2^99+2^98-2^97+…….2^2-2+1 F=3^2020-3^2019+3^2018-3^2017+…..+3^2-3+1”

1. Giải thích các bước giải:

   a.$D=1+2+2^2+…+2^{2020}$

   $\rightarrow 2D=2+2^2+2^3+…+2^{2021}$

   $\rightarrow 2D-D=2^{2021}-1$

   $\rightarrow D+1=2^{2021}$ là 1 lũy thừa

   $\rightarrow đpcm$

   b.$E=2^{100}-2^{99}+2^{98}-2^{97}+…+2^2-2+1$

   $\rightarrow 2E=2^{101}-2^{100}+2^{99}-2^{98}+..+2^3-2^2+2$

   $\rightarrow E+2E=2^{101}+1$

   $\rightarrow 3E=2^{101}+1$

   c.$F=3^{2020}-3^{2019}+3^{2018}-3^{2017}+..+3^2-3+1$

   $\rightarrow 3F=3^{2021}-3^{2020}+3^{2019}-3^{2018}+3^{2017}+..+3^3-3^2+3$

   $\rightarrow F+3F=3^{2021}+1$

   $\rightarrow 4F=3^{2021}+1$

   Bình luận