# Going Around In A Discrete Harmonic Spiral

Calculus Level 5

A man is standing at the origin. First, he walks $$1$$ unit in the positive $$x$$ direction and reaches $$(1,0)$$. Then, he turns $$60^o$$ counterclockwise and walks $$1/2$$ units. Again, he turns $$60^o$$ counterclockwise and walks $$1/3$$ units. He continues this endlessly.

Find the distance between his initial and final position.

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