2024 · Q30
If x = (1)/(2+(3)/(4+(5)/(6+(7)/(8+(9)/(10))))), then which one of the following is correct?
Elementary MathematicsNumber System
- A0
- Bx = 0.5
- C0.5
- Dx > 1.0
Explanation
Evaluating inward: 9/10 = 0.9, then 7/8.9 ≈ 0.787, 5/6.787 ≈ 0.737, 3/4.737 ≈ 0.633, giving x = 1/2.633 ≈ 0.38. The continued fraction converges rapidly to this value. Since 0 < 0.38 < 0.5, the answer is option (a).