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Consider the sequence \((u_n)\) defined for all \(n \ge 1\) by$$u_n = 3 + \frac{(-1)^n}{n^2}.$$
  1. Show that for all \(n \ge 1\), \(3 - \frac{1}{n^2} \le u_n \le 3 + \frac{1}{n^2}\).
  2. Deduce the limit of the sequence \((u_n)\) as \(n \to +\infty\).

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