Plotting $f(x) = x\lfloor 1/x \rfloor$ I want to plot $f(x) = x\lfloor 1/x \rfloor$ near the point zero for finding its limit but I can't choose proper intervals and plot it . 

This is what I obtain from GeoGebra:

No matter how much I zoomed in, I eventually ended up with a similar looking pattern so I suppose there is no 'appropriate' interval to plot this function.
Using Wolfram|Alpha, I get the series representation
$$x\left\lfloor{\frac 1x}\right\rfloor=1 - \frac x2 + \frac x\pi \sum_{k=1}^\infty \frac{\sin\left(\frac{2 k \pi}{x}\right)}{k}$$
which confirms the suspicion that
$$\lim_{x\to0}x\left\lfloor{\frac 1x}\right\rfloor=1$$
 but I have no idea how the series is derived. 
Did some research just now and it looks like the series can be quite easily obtained.
