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A sequence is defined by \(u_1 = 1\) and the recurrence relation \(u_{n+1} = \sqrt{u_n + 2}\) for all \(n \in \mathbb{Z}^+\).
Prove that the sequence \((u_n)\) is bounded above by 2, i.e., that \(u_n \le 2\) for all \(n \in \mathbb{Z}^+\).
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