# 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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