Deduce that $\mathbb{P}\left(S_n \leqslant \ell\right)$ tends to 0 when $n \rightarrow +\infty$ and that $$\mathbb{E}(N(0,\ell)) \leqslant \frac{e^{\ell}}{1 - \mathbb{E}(\exp(-X))}$$
Deduce that $\mathbb{P}\left(S_n \leqslant \ell\right)$ tends to 0 when $n \rightarrow +\infty$ and that
$$\mathbb{E}(N(0,\ell)) \leqslant \frac{e^{\ell}}{1 - \mathbb{E}(\exp(-X))}$$