# A familiar sequence

In the above circuit, each resistor has a resistance of 1 $$\Omega$$ and the wires have no resistance.

As the number of resistors approaches infinity, the equivalent resistance approaches $$\dfrac{a + \sqrt{b}} { c},$$ where $$a$$, $$b$$, and $$c$$ are positive integers, and $$b$$ is square free. What is $$a + b + c$$?

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