1/(1+1/(2+1/(3+1/(4+1/(5+1/...))))) What is the following expression's value? $\displaystyle \frac{1}{1 + \frac{1}{2 + \frac{1}{3 + \frac{1}{4 + \frac{1}{5 + \frac{1}{...}}}}}}$ 
0.697774657964... (see this WA link) 
How did you prove it? Quote:

I didn't prove it. I just used Google. 
Quote:

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