2017 · Q35
The value of √(1+√(1+√(1+...)))
Elementary MathematicsNumber System
- AEquals to 1
- BLies between 0 and 1
- CLies between 1 and 2
- DIs greater than 2
Explanation
Let L = √(1+√(1+⋯)); then L² = 1+L, so L = (1+√5)/2 ≈ 1.618 (the positive root). Thus 1 < L < 2. Hence option (C).