How would I show that the vector space $\displaystyle \ell^1 $ with the 2 norm $\displaystyle ||\cdot||_2 $is not a Banach space?

$\displaystyle \ell ^1= ( (x_i)^\infty_{i=1} : \Sigma^\infty_{i=1}|x_i|< \infty)$

I would perhaps have to show that it doesn't converge in the appropriate norm..? I am not sure how..!