# Triangle Circuit

A circuit is built by connecting $$1\ \Omega$$ wires in a pattern of triangles, as shown above. Point $$A$$ is the common vertex of all triangles, and point $$B$$ is a vertex of one of the triangles at the end of the pattern.

Let $$n$$ be the number of triangles in the pattern. (In the diagram above, $$n = 7$$.)

Determine the resistance between points $$A$$ and $$B$$ in the limit where the pattern of wires grows to infinitely many triangles, i.e. $\lim_{n\to\infty} R_{AB}$

Give your answer to 3 decimal places.

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