Conclude that
$$\frac { E \left( N _ { n } \right) } { n } \underset { n \rightarrow + \infty } { \longrightarrow } P ( R = + \infty ) .$$
One may admit and use Cesàro's theorem: if $\left( u _ { n } \right) _ { n \in \mathbb{N}^{*} }$ is a real sequence converging to the real number $\ell$, then
$$\frac { 1 } { n } \sum _ { k = 1 } ^ { n } u _ { k } \underset { n \rightarrow + \infty } { \longrightarrow } \ell .$$