Question

Arătați ca : 1/2×3/4×5/6×7/8×...×49/50<2/3×4/5×6/7×...×50/51<3/4×5/6×7/8×...×51/52
urgent ​

Answer 1

Explicație pas cu pas:

folosim formula:

$\boxed{ \bf\frac{n}{n + 1} < \frac{n + 1}{n + 2}}$

atunci:

$\frac{1}{2} < \frac{2}{3} < \frac{3}{4} \\ \frac{3}{4} < \frac{4}{5} < \frac{5}{6} \\ \frac{5}{6} < \frac{6}{7} < \frac{7}{8} \\ .... \frac{49}{50} < \frac{50}{51} < \frac{51}{52}$

înmulțim membru cu membru (pe verticală):

$\frac{1}{2} \cdot \frac{3}{4} \cdot \frac{5}{6} \cdot ... \cdot \frac{49}{50} < \frac{2}{3} \cdot \frac{4}{5} \cdot \frac{6}{7} \cdot ... \cdot \frac{50}{51} < \frac{3}{4} \cdot \frac{5}{6} \cdot \frac{7}{8} \cdot ... \cdot \frac{51}{52}$

q.e.d.