The limit superior of $|\sum_{i=1}^n x_i^k|^{1/k}$ where $x_i\in\mathbb{C}$
Doubt about step of the proof that $\limsup\limits_{n\to\infty}\left|\sum\limits_{\ell=1}^mz^n_\ell\right|^{1/n}=\max\limits_{1\le\ell\le m}|z_\ell|$