Giá trị của biểu thức : 1/1.3 + 1/3,5 + 1/5.7 + 1/7.9 + ... + 1/2021.2023 là

* Hướng dẫn giải

Đáp án A

$$\begin{gathered} \frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{2021.2023} \\ =\frac{1}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{2021.2023}\right) \\ =\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...-\frac{1}{2021}+\frac{1}{2021}-\frac{1}{2023}\right) \\ =\frac{1}{2}\left(1-\frac{1}{2023}\right) \\ =\frac{1}{2}\left(\frac{2023}{2023}-\frac{1}{2023}\right) \\ =\frac{1}{2}.\frac{2022}{2023} \\ =\frac{1011}{2023} \end{gathered}$$