If $n\rightarrow \infty, h_n\rightarrow 0$ and $n h_n\rightarrow 0$, then $n=o(1/h)$.

Question

This is the basic question: If $n\rightarrow \infty$ and $ h_n\rightarrow 0$ but I want that $n h_n\rightarrow 0$, then I must impose $n=o(1/h_n)$? See little-oh notation.

Since I want that $nh_n=o(1)$, then $n$ satisfies $n=1/h_n o(1)=o(1/h_n)$. Is this right?