\(C=\dfrac{2\cdot2022}{1+\dfrac{1}{1+2}+\dfrac{1}{1+2+3}+...+\dfrac{1}{1+2+3+...+2022}}\)
\(=\dfrac{2\cdot2022}{1+\dfrac{1}{2\cdot\dfrac{3}{2}}+\dfrac{1}{3\cdot\dfrac{4}{2}}+...+\dfrac{1}{2022\cdot\dfrac{2023}{2}}}\)
\(=\dfrac{2\cdot2022}{\dfrac{2}{2}+\dfrac{2}{2\cdot3}+...+\dfrac{2}{2022\cdot2023}}\)
\(=\dfrac{2022}{\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+...+\dfrac{1}{2022\cdot2023}}\)
\(=\dfrac{2022}{1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{2022}-\dfrac{1}{2023}}\)
\(=2022:\dfrac{2022}{2023}=2023\)
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