Finding ee through aa

Calculus Level 3

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

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

Notation: e2.71828e \approx 2.71828 denotes the Euler's number.

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