Giải thích các bước giải:
$A = \dfrac{1}{3.5} + \dfrac{1}{5.7} + \dfrac{1}{7.9} + ... + \dfrac{1}{97.99}$
$= \dfrac{1}{2}.\left ( \dfrac{2}{3.5} + \dfrac{2}{5.7} + \dfrac{2}{7.9} + ... + \dfrac{2}{97.99} \right )$
$= \dfrac{1}{2}.\left ( \dfrac{1}{3} - \dfrac{1}{5} + \dfrac{1}{5} - \dfrac{1}{7} + \dfrac{1}{7} - \dfrac{1}{9} + ... + \dfrac{1}{97} - \dfrac{1}{99} \right )$
$= \dfrac{1}{2}.\left ( 1 - \dfrac{1}{99} \right )$
$= \dfrac{1}{2}.\dfrac{98}{99}$
$= \dfrac{49}{99}$
