Explicație pas cu pas:
suma are 20-6+1 = 15 termeni
[tex]\frac{1}{20} < \frac{1}{6} \leqslant \frac{1}{6} \\ \frac{1}{20} < \frac{1}{7} < \frac{1}{6} \\ \frac{1}{20} < \frac{1}{8} < \frac{1}{6} \\ ... \\ \frac{1}{20} \leqslant \frac{1}{20} < \frac{1}{6}[/tex]
adunăm:
[tex]15 \cdot \frac{1}{20} < \frac{1}{6} + \frac{1}{7} + \frac{1}{8} + ... + \frac{1}{20} < 15 \cdot \frac{1}{6} \\ \frac{15}{20} < \frac{1}{6} + \frac{1}{7} + \frac{1}{8} + ... + \frac{1}{20} < \frac{15}{6} \\ 0.75 < \frac{1}{6} + \frac{1}{7} + \frac{1}{8} + ... + \frac{1}{20} < 2.5[/tex]
q.e.d.
