A simple inequality in calculus? I have to solve this inequality:
$$\left(\left[\dfrac{1}{s}\right] + 1 \right)  s < 1,$$ 
where   $ 0 < s < 1 $.
I guess that $s$ must be in this range: $\left(0,\dfrac{1}{2}\right]$.But I do not know if my guess is true. If so, how I can prove it?
Thank you.

try $$\left(\left[\dfrac{1}{s}\right]  \right) < \frac{1}{s}-1$$
