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Pingback: A Converging Rabbit « Rambling Thoughts

The distance is miles. Assume the rabbit starts at the origin of the complex plane and walks on it. The rabbit’s walk can be modeled by the series

,

which converges to (according to Wolframalpha). So the distance to the origin is .

I’ve now noticed that you have already posted a solution.

After reading your post I recognize that the above series is a geometric series with ratio .