\(P=\dfrac{1}{1.3}+\dfrac{1}{3.5}+\dfrac{1}{5.7}+...+\dfrac{1}{2021.2023}\)
\(=2.\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{2021}-\dfrac{1}{2023}\right)\)
\(=2.\left(1-\dfrac{1}{2023}\right)\)
\(=\dfrac{4044}{2023}\)
Ta có:
\(x.P=\dfrac{2022}{2023}\)
\(\Rightarrow x.\dfrac{4044}{2023}=\dfrac{2022}{2023}\)
\(x=\dfrac{2022}{2023}:\dfrac{4044}{2023}\)
\(x=\dfrac{1}{2}\)
Vậy \(x=\dfrac{1}{2}\)
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