limits - How to compute $lim_{nrightarrowinfty}e^{-n}left(1+n+frac{n^2}{2!}cdots+frac{n^n}{n!}right)$

There is a probabilistic method to solve it. But I am not familiar with probability. I am trying to compute it by analytic method, such as using L Hospital's rule or Stolz formula, but they are not working.