Finding \(e\) through \(a\)

Calculus Level 3

\[\displaystyle \large \lim_{n \to \infty} \left(\frac{n + a}{n - a}\right)^n = e\]

Find the value of \(a\) that satisfies the equation above. If the answer can be expressed as \(\dfrac mn\) for positive integers \((m, n)\), enter your answer as \(\left(\sqrt{n + \sqrt{m}}\right)^n\).

Notation: \(e \approx 2.71828\) denotes the Euler's number.

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