Find the value of ​

Let \(x = \cfrac{1}{1 + \cfrac{1}{2 + \cfrac{1}{1 + \cfrac{1}{2 + \dotsb}}}}\)

Then x = 1/(x + 1) ==> x^2 + x - 1 = 0 ==> x = (sqrt(5) - 1)/2

I get the following:

c=0;m=0;p=0;a=listfor(n, 1, 10,listforeach(m, d=reverse(1,2),(c=1/(c + m))
=Sqrt(3) - 1 = 0.7320508076