Question

A = 2/1 nhân 3+2/3 nhân 5 +2/3 nhân7 +...+2/2021 nhân 2023

Answer 1

\(A=\dfrac{2}{1.3}+\dfrac{2}{3.5}+...+\dfrac{2}{2021.2023}\)

\(\Rightarrow A=1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{2021}-\dfrac{1}{2023}\)

\(\Rightarrow A=1-\dfrac{1}{2023}\)

\(\Rightarrow A=\dfrac{2022}{2023}\)

Answer 2

\(A=\dfrac{2}{1}.3+\dfrac{2}{3}.5+\dfrac{2}{3}.7+...+\dfrac{2}{2021}.2023\)

\(A=\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{3.7}+...+\dfrac{2}{2021.2023}\)

\(A=1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{3}-\dfrac{1}{7}+...+\dfrac{1}{2021}-\dfrac{1}{2023}\)

\(A=1-\dfrac{1}{2023}\)

\(A=\dfrac{2022}{2023}\)