> 
> Let $c\_1 = 2$, and for $n > 1$, let $c\_n = \sqrt{1+c\_{n-1}}$. Prove:
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> 1. (by induction) that $c\_n < 2$, for $n > 1$.
> 2. (by induction) that {$c\_n$} is monotonically decreasing.
> 3. that the sequence {$c\_n$} converges.
> 4. What does the sequence converge to?
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I'm not sure how to approach this problem, let alone how to do it. Any help would be much appreciated.