$\frac{1}{5.7}$ + $\frac{1}{7.9}$ + ... +$\frac{1}{2019.2021}$
= ($\frac{1}{2}$ )$\frac{2}{5.7}$ + $\frac{2}{7.9}$ + ... +$\frac{2}{2019.2021}$
= ($\frac{1}{2}$)($\frac{1}{5}$ - $\frac{1}{7}$ + $\frac{1}{7}$ - $\frac{1}{9}$ + ... +$\frac{1}{2019}$ - $\frac{1}{2021}$)
= $\frac{1}{2}$ . ( $\frac{1}{5}$ - $\frac{1}{2021}$ )
= $\frac{1}{2}$ . $\frac{2016}{10105}$ = $\frac{1008}{10105}$