Find the norm $\| x \|$ of $x=\left( 1, -\frac{1}{3}, \frac{1}{9}, -\frac{1}{27}, \frac{1}{81}, \ldots, \frac{1}{(- 3) ^{n-1}}, \ldots \right)$ in $\ell_2$.

$\|x\|=$ .