Avem următoarea situație:
[tex]\frac{1}{10} \leq \frac{1}{10} \\ \\ \frac{1}{11}<\frac{1}{10} \\ \\ \frac{1}{12}<\frac{1}{10} \\ \\ \frac{1}{13}<\frac{1}{10} \\ \\ ............. \\ \\ \frac{1}{21}<\frac{1}{10} \\ _______________\text{ (adunam inegalitatile)}[/tex]
[tex]\underbrace{\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+...+\frac{1}{21}}_{\text{12 termeni}}<\underbrace{\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+...+\frac{1}{10}}_{\text{de 12 ori}}[/tex]
[tex]\displaystyle \frac{1}{10}+\frac{1}{11}+\frac{1}{12}+...+\frac{1}{21}<\frac{12}{10}=\frac{6}{5}[/tex]
