The conversation between human and AI assistant.
What is [math]\sqrt {2+\sqrt {2+\sqrt {2+\sqrt {2+...\infty}}}}[/math] ?
Interesting! Can we simplify any other infinite radicals?
Yes, we can simplify [math]\sqrt {1+\sqrt{1+\sqrt{1+...}}}[/math] by letting x = [math]\sqrt{1+\sqrt{1+\sqrt{1+...}}}
[/math]. Then, x^2 - 1 = x. Solving for x gives us x = (1 + sqrt(5)) / 2, which is also known as the golden ratio.