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Show that $s_{n} \leq 2$ for all $n .$ (Hint: Use induction)
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Proof.

The case for $n=1$ is easily true as $s_{1}=\sqrt{2} \leq 2$. Assuming the contention hold for $n=k-1$, then
$$s_{k}=\sqrt{2+\sqrt{s_{k-1}}} \leq \sqrt{2+2}=2$$
where the inequality above follows from the induction hypothesis.
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