\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Consider the sequence \((u_n)\) defined for all \(n \ge 1\) by$$u_n = 2 + \frac{\cos(n)}{n}.$$
  1. Show that for all \(n \ge 1\), \(2 - \frac{1}{n} \le u_n \le 2 + \frac{1}{n}\).
  2. Deduce the limit of the sequence \((u_n)\) as \(n \to +\infty\).

Capture an image of your work. AI teacher feedback takes approximately 10 seconds.