Question

2^x+2^x+1+2^x+2+...+2^x+2020=2^x+2024-8

Answer 1

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Answer 2

Lời giải:

$2^x+2^{x+1}+2^{x+2}+....+2^{x+2020}=2^{x+2024}-8$

$2^x(1+2+2^2+...+2^{2020})=2^{x+2024}-8$

$2^x(2+2^2+2^3+...+2^{2021})=2^{x+2025}-16$

$\Rightarrow 2^x(2+2^2+2^3+...+2^{2021})- (2^x(1+2+2^2+...+2^{2020}))=2^{x+2025}-16-(2^{x+2024}-8)$

$\Rightarrow 2^x(2^{2021}-1)=2^{x+2025}-2^{x+2024}-8$

$\Rightarrow 2^x(2^{2021}-1)=2^{x+2024}(2-1)-8$

$\Rightarrow 2^{x+2021}-2^x=2^{3+2021}-2^3$

$\Rightarrow x=3$