In this subsection, $X$ is a random variable taking values in $\mathbb{N}$ such that $\mathbb{P}(X = 0) > 0$. For all $k \in \mathbb{N}^{*}$, show: $1 + \sum_{j=1}^{k} \left|\lambda_{j}\right| \leqslant \frac{1}{\mathbb{P}(X = 0)^{k}}$.
In this subsection, $X$ is a random variable taking values in $\mathbb{N}$ such that $\mathbb{P}(X = 0) > 0$.
For all $k \in \mathbb{N}^{*}$, show: $1 + \sum_{j=1}^{k} \left|\lambda_{j}\right| \leqslant \frac{1}{\mathbb{P}(X = 0)^{k}}$.