So, my professor me gave this exercise as a challenge:
-First, prove that:
$$1+{1\over 1+{1\over 1+{1\over 1+{1\over 1+...}}}}={1+\sqrt{5}\over 2}.$$
-Then, prove that:
$$1+{1\over 1+{1\over 1+{1\over 1+{1\over 1+...}}}}=\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+...}}}}$$
He said you need no advanced maths to solve it: you just need high-school math with no calculus...
The thing is that it's been 2 weeks now and I'm as lost as when I first saw the problem.
Can someone help me!
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