Question

mare nevoie de ajutor, va rog sa dati explicatie

Answer 1

Răspuns:

$\displaystyle{ x= (1 + \frac{1}{2})(1+\frac{1}{3})(1+\frac{1}{4}) }$

$\displaystyle{ x = (1 + \frac{1}{3} + \frac{1}{2} + \frac{1}{6})(1 + \frac{1}{4}) }$

$\displaystyle{ x = (1 + \frac{2+3}{6} + \frac{1}{6})(1 + \frac{1}{4}) }$

$\displaystyle{ x = 2 \cdot (1 + \frac{1}{4}) = 2 + \frac{2}{4} }$

$\displaystyle{ x = 2 + \frac{1}{2} = \frac{5}{2} = 2,5 }$

$\displaystyle{ y = (1 - \frac{1}{2})(1-\frac{1}{3})(1-\frac{1}{4}) }$

$\displaystyle{ y= (1 - \frac{1}{3} - \frac{1}{2} + \frac{1}{6})(1 - \frac{1}{4}) }$

$\displaystyle{ y = \frac{1}{3} \cdot (1 - \frac{1}{4}) = \frac{1}{3} - \frac{1}{12} }$

$\displaystyle{ y = \frac{4-1}{12} = \frac{3}{12} = \frac{1}{4} = 0,25 }$

$\displaystyle{ x > y > 0 }$

(D)