\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
A sequence is defined by \(u_0 = 2\) and the recurrence relation \(u_{n+1} = \frac{u_n}{3} + 2\) for all \(n \in \mathbb{N}\).
Prove that the sequence \((u_n)\) is increasing, i.e., that \(u_{n+1} \ge u_n\) for all \(n \in \mathbb{N}\).
Capture an image of your work. AI teacher feedback takes approximately 10 seconds.