Solution
= Solution
{c}
The set $S=\{x_n:x_n\ne\ell\}$ is countable, hence closed, and does not contain $\ell$. Its complement is an open neighborhood of $\ell$. Convergence therefore places every sufficiently late term outside $S$, which is possible only if those terms equal $\ell$. Thus \b[the <sequence> is eventually constant at its limit], and the set of exceptional indices is finite. This conclusion concerns repeated indices as well as distinct values.