Solution
= Solution
For $1<p<\infty$, truncation makes the $\ell^p$ tail arbitrarily small, since $\sum_j|a_j|^p$ converges. Approximate the finite remaining coordinates by numbers in $\mathbb Q+i\mathbb Q$. The resulting countable set of <finitely supported sequences> is dense. Therefore
$$
\boxed{\ell^p\text{ is separable for }1<p<\infty.}
$$
The same construction also works for $p=1$, though that endpoint is not needed here.