Infinite triangular Resistance

Determine the resistance RAB{ R }_{ AB } between the points A and B of the frame made of thin homogeneous wire (as shown in figure), assuming that the number of successively embedded equilateral triangles (with sides decreasing by half) tends to infinity. Side ABAB is equal to aa units and the resistance of unit length of wire is ρ\rho units.

If the resistance RAB{ R }_{ AB } is of the form aρ(dcf)a\rho \left( \dfrac { \sqrt { d } -c }{ f } \right) , find d+c+fd+c+f.

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