Many mathematicians know that: $$\phi = 1 + \cfrac{1}{1 + \cfrac{1}{1 + \cfrac{1}{1 + \cfrac{1}{1 + \ddots}}}}$$ as a continued fraction. But do you know why?
Here are some problems on the theme 'continued':
1) Evaluate $\sqrt{3\sqrt{3\sqrt{3\cdots}}}$
2) Evaluate $\sqrt{3+\sqrt{3+\sqrt{3+\cdots}}}$
3) Evaluate $\frac{\frac{\frac{a+1}{2}+1}{2}+1}{2}+1\cdots$
