Giải thích các bước giải:
$A = \dfrac{1}{1.3} + \dfrac{1}{3.5} + \dfrac{1}{5.7} + ... + \dfrac{1}{97.99} + \dfrac{1}{99.101}$
$= \dfrac{1}{2}.\left ( \dfrac{2}{1.3} + \dfrac{2}{3.5} + \dfrac{2}{5.7} + ... + \dfrac{2}{97.99} + \dfrac{2}{99.101} \right )$
$= \dfrac{1}{2}.\left ( 1 - \dfrac{1}{3} + \dfrac{1}{3} - \dfrac{1}{5} + \dfrac{1}{5} - \dfrac{1}{7} + ... + \dfrac{1}{97} - \dfrac{1}{99} + \dfrac{1}{99} - \dfrac{1}{101} \right )$
$= \dfrac{1}{2}.\left ( 1 - \dfrac{1}{101} \right )$
$= \dfrac{1}{2}.\dfrac{100}{101}$
$= \dfrac{50}{101}$
