Power Limit!

Calculus Level 5

\[\large{L = \lim_{n \to \infty} \left( \dfrac{2n(e-e_n)}{e} \right)^{-n} \quad; \quad e_n = \left( 1 + \dfrac{1}{n} \right)^n}\]

If \(L\) can be expressed as \(\large{e^{A/B}}\) for positive coprime integers \(A,B\), submit the value of \(A+B\) as your answer.

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