The Recursion Is Trapped In The Exponent!

Calculus Level 2

The sequence \(\{ {a}_{n}\} \) satisfies \( \left(\frac{2n+1}{2n-1}\right)^{a_n} =e^2.\) Find \( \lim_{n \rightarrow \infty}\frac{2a_n}{n+1} \).

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