Giải thích các bước giải:
$\dfrac{3}{9.14} + \dfrac{3}{14.19} + ... + \dfrac{3}{(5n - 1)(5n + 4)}$
$= \dfrac{3}{5}\left ( \dfrac{5}{9.14} + \dfrac{5}{14.19} + ... + \dfrac{5}{(5n - 1)(5n + 4)} \right )$
$= \dfrac{3}{5}\left ( \dfrac{1}{9} - \dfrac{1}{14} + \dfrac{1}{14} - \dfrac{1}{19} + ... + \dfrac{1}{5n - 1} - \dfrac{1}{5n + 4} \right )$
$= \dfrac{3}{5}\left ( \dfrac{1}{9} - \dfrac{1}{5n + 4} \right )$
$= \dfrac{1}{15} - \dfrac{3}{5}.\dfrac{1}{5n + 4} < \dfrac{1}{15}$