Multiple choice general knowledge math & puzzles

Find the value of (1/(6+1/(2+1/(6+1/(2+1/....)))))

  1. (-3+2*3^(0.5))/3

  2. 1

  3. Cannot be determined

  4. (-3-2*3^(0.5))/3

  5. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The continued fraction x = 1/(6+1/(2+1/(6+1/(2+...)))) can be solved by noting the periodic pattern. Let x = 1/(6+1/(2+x)), which leads to a quadratic equation. Solving gives x = (-3+2√3)/3, which matches option A in decimal form.

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