>>12719738Look at the sequence of functions 1, 1/(x+2), 1/(x+2/(x+3)), ...
Notice you keep modifying the bottom right term.
Consider the sequence, z, 1/(x+2z), 1/(x+2/(x+3z)), ...
Going from first term to second, z is replaced by 1/(x+2z)
Going from second term to third, z is replaced by 1/(x+3z)
Etc.
Each time you perform a mobius transformation.
This can be represented by an infinite product of 2x2 matrices.
https://en.wikipedia.org/wiki/M%C3%B6bius_transformation#Projective_matrix_representations[a,b;c,d] corresponds to (az+b)/(cz+d).
Notice you can rescale a,b,c,d by a common factor to get the same mobius transformation.
find the mobius transformation associated with the infinite product of matrices:
[0,1;2,x]*[0,1;3,x]*[0,1;4,x]...
and plug in z=1 or something (you might need z=0 or z=1/x).
