Question

$\underset{x\to 0^{+}}{\lim }x\left(\left[\frac{1}{x}\right]+\left[\frac{2}{x}\right]+.....+\left[\frac{15}{x}\right]\right)$ 
$\underset{x\to 0^{+}}{\lim }x\left(\frac{1+2+3+....+15}{x}\right)-\left(\left\{\frac{1}{x}\right\}+\left\{\frac{2}{x}\right\}+.....+\left\{\frac{15}{x}\right\}\right)$
$\because 0 \le \left\{\frac{r}{x}\right\} < 1$
$0 \le \left\{\frac{r}{x}\right\} < x$
$\underset{x\to 0^{+}}{\lim }x\left(\frac{1+2+3+....+15}{x}\right)=\frac{15.16}{2}=120$