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Let \((u_n)\) be the sequence defined for \(n \ge 1\) by \(u_{n} = 1 - \dfrac{1}{n^2}\).
  1. Show that \((u_n)\) is bounded above by \(1\).
  2. Show that \((u_n)\) is increasing.
  3. Conclude that \((u_n)\) converges.

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