2019 · Q41
What is the value of 2 + √(2 + √(2 + √(2 + ...)))?
Elementary MathematicsAlgebra
- A1
- B2
- C3
- D4
Explanation
Let S = √(2+√(2+…)). Then S = √(2+S), so S^2 − S − 2 = 0 gives S = 2 (positive root). The expression is 2 + 2 = 4.
What is the value of 2 + √(2 + √(2 + √(2 + ...)))?
Explanation
Let S = √(2+√(2+…)). Then S = √(2+S), so S^2 − S − 2 = 0 gives S = 2 (positive root). The expression is 2 + 2 = 4.