Question

Calculati:
$\lim_{n \to \ }_{0} , n_{<0} {(n/3)*[2/n]$ , Unde [2/n], reprezinta partea intreaga a lui 2/n

Answer 1

$\frac{2}{n} -1<[ \frac{2}{n} ] \leq \frac{2}{n}| \cdot \frac{n}{3} => \frac{2-n}{3} < \frac{n}{3} \cdot [ \frac{2}{n} ] \leq \frac{2}{3}$
Trecand la limita in inegalitatile anterioare obtinem valorea limitei $\frac{2}{3}$.