A Peculiar Infinite Limit!

Calculus Level 4

\[\large{L=\lim_{n \to \infty} \left[ (n+1)! \ (e^{x_{n+1}} - e^{x_{n}}) \right ] } \]

If \({x_n = \displaystyle \sum_{k=0}^n \dfrac{1}{k!}}\), then find the value of \({\ln(L)}\). Give your answer to 3 decimal places.

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