Question

Repede va rog, 15 puncte plus coroana​

Answer 1

Răspuns:

ex.29

Explicație pas cu pas:

$x = \frac{1}{2} \cdot \frac{3}{4} \cdot \frac{5}{6} \cdot \frac{7}{8} \cdot ... \cdot \frac{99}{100}$

$y = \frac{2}{3} \cdot \frac{4}{5} \cdot \frac{6}{7} \cdot \frac{8}{9} \cdot ... \cdot \frac{100}{101}$

=>

$x \cdot y = \Big( \frac{1}{2} \cdot \frac{3}{4} \cdot \frac{5}{6} \cdot \frac{7}{8} \cdot ... \cdot \frac{99}{100} \Big) \cdot \Big( \frac{2}{3} \cdot \frac{4}{5} \cdot \frac{6}{7} \cdot \frac{8}{9} \cdot ... \cdot \frac{100}{101} \Big)$

$= \frac{1}{ \not2} \cdot \frac{\not2}{\not3} \cdot \frac{\not3}{\not4} \cdot \frac{\not4}{\not5} \cdot \frac{\not5}{\not6} \cdot \frac{\not6}{\not7} \cdot \frac{\not7}{\not8} \cdot \frac{\not\not8}{\not9} \cdot ... \cdot \frac{\not99}{\not100} \cdot \frac{\not100}{101}$

$= \bf \frac{1}{101}$