This is essentially 3.1999 I guess. We have to use a nested floor function property to get that each term is essentially $$\lfloor\pi\rfloor$$Which is 3 times 1999 We can claim that $$\lfloor\pi\rfloor$$lies between $$\frac{\lfloor k\pi\rfloor}k$$and $$\frac{\lfloor k\pi\rfloor}k -1$$And conclude our result directly. Took more time to Latex it than to actually solve.