Ta có:
$\frac{200}{201} + \frac{201}{202}$
$= 1 - \frac{1}{201} + 1 - \frac{1}{202} $
$= 1 + (1 - \frac{1}{201} - \frac{1}{202})$
$> 1 + (1 - \frac{2}{201})$
$> 1$
Trong khi đó: Ta có: 200 + 201 < 201 + 202
$=> \frac{200+201}{201+202} < 1$
$=> \frac{200+201}{201+202} < \frac{200}{201} + \frac{201}{202}$
Vậy $\frac{200+201}{201+202} < \frac{200}{201} + \frac{201}{202}$