**EDIT:** Let $X$ be a geometrically irreducible $n$-dimensional variety over finite field $\mathbb{F}_{q_0}$. Let $\mathbb{F}_q$ denote any finite extension of $\mathbb{F}_{q_0}$.

It is known (e.g. follows from the Weil conjectures) that $$\frac{|X(\mathbb{F}_q)|}{q^n}\to 1 \mbox{ as } q\to\infty.$$ I am wondering if there is an elementary proof of this fact.