Going Around In A Discrete Harmonic Spiral

Calculus Level 5

A man is standing at the origin. First, he walks 11 unit in the positive xx direction and reaches (1,0)(1,0). Then, he turns 60o60^o counterclockwise and walks 1/21/2 units. Again, he turns 60o60^o counterclockwise and walks 1/31/3 units. He continues this endlessly.

Find the distance between his initial and final position.

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