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.