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Euge
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MHB
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Let ##\mathbb{R}^\omega_{+}## be the set of all sequences ##(a_n)_{n=1}^\infty## of positive real numbers. Determine the infimum $$\inf\left\{\limsup_{n \to \infty} \left(\frac{1 + a_{n+1}}{a_n}\right)^n : (a_n) \in \mathbb{R}^\omega_{+}\right\}$$