We assume $\lambda < 1$, and $D_{n} = \sum_{k=n+1}^{+\infty} \frac{(n\lambda)^{k}}{k!}$. Using Taylor's formula with integral remainder, deduce an equivalent of $D_{n}$ when $n \rightarrow +\infty$.
We assume $\lambda < 1$, and $D_{n} = \sum_{k=n+1}^{+\infty} \frac{(n\lambda)^{k}}{k!}$. Using Taylor's formula with integral remainder, deduce an equivalent of $D_{n}$ when $n \rightarrow +\infty$.