Is my set compact in $l^2$?

Question

I need to understand if the set provided by me is compact in $\ell^2$ or not. So I define the set $$ A = \bigl\{ x = (x_1, x_2, \ldots, x_N, 0, 0, \ldots) \in \ell^2 : \|x\|_{\ell^2} \leq 1 \bigr\}, $$ where $N$ is fixed. So I have to some kind a subset of $\mathbb{R}^N$, and $A$ is sequentially compact $\therefore$ it is compact in $\ell^2$. If the example is ok or not, can you give another simple example of compact sets in $\ell^2$. Thanks in advance.