If a sequence of reals $$(a_n)_{n=m}^{\infty}$$ converges to a real $$L$$, we say that $$(a_n)_{n=m}^{\infty}$$ is [...] and that $$L$$ is the [...]. We write:
$L = \lim_{n\to\infty}a_n$
If a sequence does not converge to a real, then it is said to [...] or be [...]. $$\lim_{n\to\infty}a_n$$ is left undefined for a divergent sequence.