A=1/1.3 +1/3.5+1/5.7+...+1/2021.2023

A = $\dfrac{1}{1 . 3}$ + $\dfrac{1}{3 . 5}$ + $\dfrac{1}{5 . 7}$ + ... + $\dfrac{1}{2021 . 2023}$

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

2A =  $\dfrac{1}{1}$ - $\dfrac{1}{3}$ + $\dfrac{1}{3}$ - $\dfrac{1}{5}$ +$\dfrac{1}{5}$ -  $\dfrac{1}{7}$ + ... +  $\dfrac{1}{2021}$ -  $\dfrac{1}{2023}$ 

2A = $\dfrac{1}{1}$ -  $\dfrac{1}{2023}$

2A = $\dfrac{2022}{2023}$ 

A = $\dfrac{2022}{2023}$ : $\text{2}$

A = $\dfrac{1011}{2023}$