Finding $\displaystyle \lim_{x\rightarrow 0}x^2\bigg(1+2+3+\cdots \cdots +\bigg\lfloor \frac{1}{|x|}\bigg\rfloor \bigg)$, where $\lfloor x \rfloor $ is a floor function of $x$
Attempt: put $\displaystyle x = \frac{1}{y}$
so $\displaystyle \lim_{y\rightarrow \infty}\frac{1+2+3+\cdots \cdots \lfloor y \rfloor }{y^2}$
could some help me