Ta có :
$\dfrac{1}{20}+\dfrac{1}{21}+\dfrac{1}{22}+...+\dfrac{1}{50}$
$=\dfrac{1}{20}+(\dfrac{1}{21}+\dfrac{1}{22}+..+\dfrac{1}{30})+(\dfrac{1}{31}+\dfrac{1}{32}+...+\dfrac{1}{40})+(\dfrac{1}{41}+\dfrac{1}{42}+...+\dfrac{1}{50})$
$>\dfrac{1}{20}+(\dfrac{1}{30}+\dfrac{1}{30}+..+\dfrac{1}{30})+(\dfrac{1}{40}+\dfrac{1}{40}+..+\dfrac{1}{40})+(\dfrac{1}{50}+\dfrac{1}{50}+..+\dfrac{1}{50})$
$=\dfrac{1}{20}+\dfrac{1}{30}\times10+\dfrac{1}{40}\times10+\dfrac{1}{50}\times10$
$=\dfrac{1}{20}+\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{5}$
$=(\dfrac{1}{20}+\dfrac{1}{5})+\dfrac{1}{3}+\dfrac{1}{4}$
$=\dfrac{1}{4}+\dfrac{1}{3}+\dfrac{1}{4}$
$>\dfrac{1}{4}+\dfrac{1}{4}+\dfrac{1}{4}=\dfrac{3}{4}$
Vậy $A>\dfrac{3}{4}$
