giúp mk với ah
a) \(A=1+\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^{2022}}\)
\(\Rightarrow2^{2022}.A=2^{2022}+\dfrac{2^{2022}}{2}+\dfrac{2^{2022}}{2^2}+...+\dfrac{2^{2022}}{2^{2022}}\)
\(\Rightarrow2^{2022}.A=2^{2022}+2^{2021}+2^{2020}+...+1\)
\(\Rightarrow2^{2022}.2.A=2^{2023}+2^{2022}+2^{2021}+...+2\)
\(\Rightarrow2^{2023}.A-2^{2022}.A=\left(2^{2023}+2^{2022}+2^{2021}+...+2\right)-\left(2^{2022}+2^{2021}+2^{2020}+...+1\right)\)
\(\Rightarrow2^{2022}.A\left(2-1\right)=2^{2023}-1\)
\(\Rightarrow A=\dfrac{2^{2023}-1}{2^{2022}}\).
-Câu b bạn làm tương tự.
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