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Consider the sequence \((u_n)\) defined for all \(n \in \mathbb{N}\) by$$u_n = n - \sin(n).$$
  1. Show that for all \(n \in \mathbb{N}\), \(u_n \ge n - 1\).
  2. Deduce the limit of the sequence \((u_n)\) as \(n \to +\infty\).

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