Ta có $\frac{1}{1}$ - $\frac{1}{2}$ = $\frac{1.2-1}{1.2}$ = $\frac{1}{1.2}$
$\frac{1}{2}$ - $\frac{1}{3}$ = $\frac{1.3-1.2}{2.3}$ = $\frac{1}{2.3}$
$\frac{1}{3}$ - $\frac{1}{4}$ = $\frac{1.4-1.3}{3.4}$ = $\frac{1}{3.4}$
$\frac{1}{49}$ - $\frac{1}{50}$ = $\frac{1.50-1.49}{49.50}$ = $\frac{1}{49.50}$
Mấy số khác cũng tương tự nên ta có
$\frac{1}{1.2}$ + $\frac{1}{2.3}$ + $\frac{1}{3.4}$ + ... + $\frac{1}{49.50}$
= $\frac{1}{1}$ - $\frac{1}{2}$ + $\frac{1}{2}$ - $\frac{1}{3}$ + $\frac{1}{3}$ - $\frac{1}{4}$ + ... + $\frac{1}{49}$ - $\frac{1}{50}$
= $\frac{1}{1}$ - $\frac{1}{50}$
= $\frac{1.50-1.1}{1.50}$
= $\frac{49}{50}$