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1951 AMC 12 Question 42

AMC12 · 1951 AMC 12

Question 42

If $x$ equals $$
\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\cdots}}}},
$$ then:
  1. $x=1$
  2. $0\lt x\lt1$
  3. $1\lt x\lt2$
  4. $x$ is infinite
  5. $x\gt2$ but finite