How does one calculate $$\lim_{n\to\infty}e^{-n}\sum_{k=0}^{n-1}\frac{n^k}{k!}?$$ Numerically it is somewhat close to $\frac12$. But to prove that I am going around a circle! Thanks for any help.
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Hint: Taylor series of $e^x$ is $\displaystyle\sum_{k=0}^\infty \dfrac{x^k}{k!}$ – Prasun Biswas Apr 08 '15 at 07:15