AHSME 1951 Problem 42

If $x =\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\cdots}}}}$ , then: $\textbf{(A)}\ x = 1 \textbf{(B)}\ 0 2\text{ but finite}$

Dataset text NuminaMath-1.5. Quoted with source.

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