Investigation of the resistance of an infinite rectangular circuit

The following problem was proposed in 2016 at the all-Ukrainian Physics Olympiad An infinite circuit is given (see Fig. 1) where the resistance of each horizontal segment is equal to 1 Ω, and the resistance of each vertical segment is equal to 3 Ω. The task was to estimate the general resistance of the given infinite circuit between the terminals A and В. The author solution leads to the result 0,65 0,05 R    . However, the problem occurs to calculate the general resistance under consideration with higher accuracy.