Ta có $ \frac{1}{2} + \frac{1}{2.3} + \frac{1}{3.4} + ...+ \frac{1}{9.10} $
$= \frac{1}{1.2} + \frac{1}{2.3} + \frac{1}{3.4} + ...+ \frac{1}{9.10} $
$= \frac{1}{1} - \frac{1}{2} + \frac{1}{2}- \frac{1}{3} + ...+ \frac{1}{9} - \frac{1}{10} $
$=1- \frac{1}{10}$
$= \frac{9}{10} $
Vậy : $ \frac{1}{2} + \frac{1}{2.3} + \frac{1}{3.4} + ...+ \frac{1}{9.10} = \frac{9}{10} $