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AMO 2025 Junior College (Grade 11–12) Question 9

AMO · AMO 2025 Junior College (Grade 11–12)

Question 9

Let $x=\frac1{2+\frac1{2+\frac1{2+\cdots}}}$. Which expression equals $x+2$?

Question illustration
  1. $\frac1x$
  2. $\frac1{x^2}$
  3. $x^2$
  4. $\frac2x$