At every point the resistors meet would be effectively increasing the resistance. It is because any current here would only be able to see the outer path due to the presence of infinite number of triangular mesh. The outer path consists of two resistors with resistance of R each. They are in series and thus, the resultant resistance would be R+R = 2R. This is the effective resistance for such a complicated mesh.

Hi

Let equivalent resistance be x

Circuit is as shown

R_eq = 2R(R+x)/(4R+3x)   ----------------------(1)

but we assumed R_eq = x  ----------------------(2)

So from 1 and 2

x = R(7^1/2 - 1)/3

 

This is the only way to solve these type of questions