Explicație pas cu pas:
[tex]\boxed{ \bf\frac{n}{n + 1} < \frac{n + 1}{n + 2}}\\[/tex]
atunci:
[tex]\frac{1}{2} < \frac{2}{3} < \frac{3}{4} \\ \frac{3}{4} < \frac{4}{5} < \frac{5}{6} \\ \frac{5}{6} < \frac{6}{7} < \frac{7}{8} \\ .... \frac{49}{50} < \frac{50}{51} < \frac{51}{52} \\[/tex]
înmulțim membru cu membru (pe verticală):
[tex]\frac{1}{2} \cdot \frac{3}{4} \cdot \frac{5}{6} \cdot ... \cdot \frac{49}{50} < \frac{2}{3} \cdot \frac{4}{5} \cdot \frac{6}{7} \cdot ... \cdot \frac{50}{51} < \frac{3}{4} \cdot \frac{5}{6} \cdot \frac{7}{8} \cdot ... \cdot \frac{51}{52} \\[/tex]
q.e.d.
