• $\frac{2}{3} + \frac{1}{3} = 1$;
• $\frac{3}{4} +\frac{2}{4} + \frac{1}{4} =1 + \frac{2}{4} = \frac{3}{2}$;
• $\frac{4}{5} + \frac{3}{5} + \frac{2}{5} + \frac{1}{5} = (\frac{4}{5} + \frac{1}{5}) + (\frac{3}{5} + \frac{2}{5}) = 1 + 1 = 2$.
• $\frac{5}{6} + \frac{4}{6} + \frac{3}{6} + \frac{2}{6} + \frac{1}{6} = (\frac{5}{6} + \frac{1}{6}) + (\frac{4}{6} + \frac{2}{6}) + \frac{3}{6} = 1 + 1 + \frac{1}{2} = \frac{5}{2}$.
• Tính tổng:

$S = \frac{999}{1000} + \frac{998}{1000} + ... + \frac{1}{1000} = (\frac{999}{1000} + \frac{1}{1000}) + (\frac{998}{1000} + \frac{2}{1000}) + ... + (\frac{501}{1000} + \frac{499}{1000}) + \frac{500}{1000} = 1 + 1 + ... + 1 + \frac{1}{2}$.

Trong tổng trên có 499 cặp có tổng là 1 $\Rightarrow $ $S = 499 + \frac{1}{2} = \frac{999}{2}$.