Let $f(x) = \left\lfloor \frac{2 - x}{x + 5} \right\rfloor$. Evaluate f(1) + f(2) + f(3) + ... + f(999) + f(1000).
Note that
f(1) = floor [ 1/ 6 ] = 0
f(2) = floor [ 0 ] = 0
f(3) = floor [-1/8] = -1
f(4) = floor [ -2/ 9] = -1
.......
f(1000) = floor [ -998 / 1005] = -1
So the sum is [ (1000 - 3 + 1 ] (-1) = [998] (-1) = -998