\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Let \((u_n)\) be the sequence defined for \(n \ge 0\) by$$u_n=\frac{3n+1}{n+2}.$$
  1. Show that \((u_n)\) is upper bounded by \(3\).
  2. Show that \((u_n)\) is increasing.
  3. Conclude that \((u_n)\) converges.

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