In the case of the fly, von Neumann probably just calculated the length of the first and second trip and calculated the sum using the self-similarity of the ser

In the case of the fly, von Neumann probably just calculated the length of the first and second trip and calculated the sum using the self-similarity of the series. http://en.wikipedia.org/wiki/Geometric_series#Sum http://en.wikipedia.org/wiki/Geometric_series#Sum