The value of the continued fraction \(2-\frac{1}{2-\frac{1}{2-\frac{1}{\cdots}}}\)
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Correct Answer: Option A
Detailed Explanation:
Let the value of the continued fraction be x. The fraction can be written as x = 2 - 1/x because the pattern repeats infinitely.
Multiplying both sides by x: x² = 2x - 1, which rearranges to x² - 2x + 1 = 0. Factoring gives (x - 1)² = 0, so x = 1.
Therefore, the value of the continued fraction is 1, making Option 1 the correct answer.
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