Let ${\{x_i\}} \subset \mathbb{C}$, $x_i \neq 0$, $x_i \rightarrow 0$, $|x_i| < 1$.
$\xi_i$ = {$x^k_i$}$_{k\ge0} \Rightarrow$ {$\xi_i$} is complete system of sequences in $l_2$.
I should prove that every Cauchy sequence converges in $l_2$. But from definition $x_i \rightarrow 0$, why it's not enough for the proof?
Or should I find clojure of {$\xi_i$} in $l_2$(then {$\xi_i$} is dence in $l_2$).
If I'm right, what should I do next?