I've made a few plots and noticed that $\lfloor
Is it true that for positive $x > 1$ and $n \in \mathbb N,\quad n>=2$ the following holds:
$$(\lfloor x \rfloor + 1)^n >= \lfloor x^n \rfloor $$
If it is, how can it be proven? If it is not, will that at least hold when $n=2$? I am interested in the latter case, actually.