Đặt \(A=\frac{1}{1\cdot3}+\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+...+\frac{1}{2019\cdot2021}\)
\(2A=\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+....+\frac{2}{2019\cdot2021}\)
\(2A=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+....+\frac{1}{2019}-\frac{1}{2021}\)
\(2A=1-\frac{1}{2021}=\frac{2020}{2021}\)
\(A=\frac{2020}{2021}:2=\frac{2020\cdot2}{2021}=\frac{4040}{2021}\)
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Tran Le Khanh Linh lm sai r nếu chia 2 thì 2021.2 chứ ko phải 2020.2
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