Răspuns:
Explicație pas cu pas:
suma are: 20-6+1 = 15 termeni
avem:
[tex]\frac{1}{20} < \frac{1}{6} \leq \frac{1}{6}\\\frac{1}{20} < \frac{1}{7} < \frac{1}{6}\\\frac{1}{20} < \frac{1}{8} < \frac{1}{6}\\...\\\frac{1}{20} \leq \frac{1}{20} < \frac{1}{6}\\[/tex]
adunam relatiile:
[tex]15 \cdot \frac{1}{20} < \frac{1}{6} + \frac{1}{7} + \frac{1}{8} + ... + \frac{1}{20} < 15 \cdot \frac{1}{6}[/tex]
[tex]\frac{3}{4} < \frac{1}{6} + \frac{1}{7} + \frac{1}{8} + ... + \frac{1}{20} < \frac{5}{2}[/tex]
[tex]0,75 < \frac{1}{6} + \frac{1}{7} + \frac{1}{8} + ... + \frac{1}{20} < 2,50[/tex]
q.e.d.
