Golden ratio and limits of two sequences

Abstract

We prove that the golden ratio can be obtained as a limit of two sequences: \sqrt{1}, \sqrt{1+\sqrt{1}}, \sqrt{1+\sqrt{1+\sqrt{1}}}, ... a 2/1, 3/2, 5/3, 8/5, ...

Keywords

• golden ratio
• golden section
• golden number
• sequence
• Fibonacci sequence