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Set Theorymedium
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For each positive integer n≥1n \ge 1n≥1, let AnA_nAn​ be the interval of real numbers defined as An={x∈R:3−1n≤x<7+2n}A_n = \{x \in \mathbb{R} : 3 - \frac{1}{n} \le x < 7 + \frac{2}{n}\}An​={x∈R:3−n1​≤x<7+n2​}. Determine the intersection of this infinite family of sets, ⋂n=1∞An\bigcap_{n=1}^{\infty} A_n⋂n=1∞​An​.