Ta có : $A=\frac{20}{1.3.5} + \frac{20}{3.5.7} +...+ \frac{20}{19.21.23}$ $
$=5.(\frac{4}{1.3.5} + \frac{5}{3.5.7} +...+ \frac{5}{19.21.23}$ ) $
$= 5.(\frac{1}{1.3} - \frac{1}{3.5} + \frac{1}{3.5} - \frac{1}{5.7}+...+ \frac{1}{19.21}$-\frac{1}{21.23} ) $
$=5.(\frac{1}{1.3} - \frac{1}{21.23} ) $
$=5. \frac{160}{483} = \frac{800}{483} $
Vậy : $A=\frac{800}{483} $
Chúc bạn học tốt !