Show that the following three assertions are equivalent\\
(i) $R_u = +\infty$,\\
(ii) $\mathbb{M}_n(u) = \mathscr{M}_n(\mathbb{C})$,\\
(iii) $\mathbb{M}_n(u) \neq \emptyset$ and $\forall A \in \mathbb{M}_n(u), \forall B \in \mathbb{M}_n(u), A + B \in \mathbb{M}_n(u)$,\\
and give an example of a sequence $u$ satisfying these three assertions and such that $u_k \neq 0$ for every $k \in \mathbb{N}$.