Problem

Source: Ukraine 1999 Grade 10 P5

Tags: algebra, floor function



Evaluate $$\lfloor\pi\rfloor+\left\lfloor\frac{\lfloor2\pi\rfloor}2\right\rfloor+\left\lfloor\frac{\lfloor3\pi\rfloor}3\right\rfloor+\ldots+\left\lfloor\frac{\lfloor1999\pi\rfloor}{1999}\right\rfloor.$$