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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