$S\_F$ is the space of real sequences $\mathbf a=(a\_n)\_{n=1}^{\infty}$ such that every sequence $\mathbf a\in S\_F$ is eventually zero. $\|\cdot\|\_1$ is the norm defined as $\|\mathbf a\|\_1=\sum\_{n=1}^{\infty}\lvert a\_n\rvert$.

I know that a Banach space is one where every Cauchy sequence in $S\_F$ converges to an element of $S\_F$ but I don't know how to prove that a normed vector space is not Banach. Can anyone help?