\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Consider the sequence \((u_n)\) defined for \(n \ge 2\) by \(u_n=\dfrac{3n-2}{n-1}\).
  1. Show that using the quotient rule directly leads to an indeterminate form.
  2. Show that for all \(n \ge 2\), \(u_n=\dfrac{3-\frac{2}{n}}{1-\frac{1}{n}}\).
  3. Deduce the limit of the sequence \((u_n)\).

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