Have you reached your limit?

Calculus Level 5

\[\large\displaystyle\lim_{n \to \infty} \left(e^{-n} \sum_{k=0}^{n} \dfrac{n^{k}}{k!}\right) = \dfrac{a}{b} \]

In the above equation, \(a\) and \(b\) are positive coprime integers. Find \(a + b\).

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