closed convex hull of $\{e_n:n\in \mathbb N\}$ in $\ell^1$

Question

I want to get s description of the set $\overline{co}(\{e_1,e_2,\ldots,e_n,\ldots\})$ in $\ell^1$.

We know that in a normed linear space, closed convex hull of a set is the closure of the convex hull of the set. We have $co(\{e_1,e_2,\ldots\})=\{\sum\limits_{i=1}^n\lambda_ie_i:\lambda_i\geq 0, \sum\limits_{i=1}^n\lambda_i=1\}$. Now how to express its closure? Any suggestion will be appreciated.