Golden ratio is a root of x2-x-1=0. That is,
x2=x+1
Divided by x, we get
We then recursively plug in x=1+1/x to x on the right hand side.
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where we can do it more.
Similarly, silver ratio is a root of x2-2x-1. That is,
x2=2x+1.
Divided by x, we get
We then recursively plug in x=2+1/x to x on the right hand side.
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and so on.
In general, for some quadratic function a*x2+b*x+c=0,
for 
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