a: \(A=\dfrac{1}{3}\left(\dfrac{3}{1\cdot4}+\dfrac{3}{4\cdot7}+...+\dfrac{3}{2020\cdot2023}\right)\)
\(=\dfrac{1}{3}\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+...+\dfrac{1}{2020}-\dfrac{1}{2023}\right)\)
\(=\dfrac{1}{3}\cdot\dfrac{2022}{2023}=\dfrac{674}{2023}\)
c: \(D=\dfrac{1}{2}+\dfrac{1}{4}+...+\dfrac{1}{2^{2022}}\)
\(\Leftrightarrow2D=1+\dfrac{1}{2}+...+\dfrac{1}{2^{2021}}\)
\(\Leftrightarrow D=1-\dfrac{1}{2^{2022}}=\dfrac{2^{2022}-1}{2^{2022}}\)
\(C=\dfrac{2^{2022}}{2^{2022}-1}\cdot\dfrac{2^{2022}-1}{2^{2022}}=1\)
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