# Infinite triangular Resistance

Determine the resistance $${ R }_{ AB }$$ 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 $$AB$$ is equal to $$a$$ units and the resistance of unit length of wire is $$\rho$$ units.

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

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