Let $L_1$, $L_2$, $L_3$, $\dots$ be an infinite sequence of context-free languages, each of which is defined over a common alphabet $Σ$. Let $L$ be the infinite union of $L_1$, $L_2$, $L_3$, $\dots $; i.e., $L = L_1 \cup L_2 \cup L_3 \cup \dots $.
Is it always the case that $L$ is a context-free language?