each succeeding term x_{n+1}is produced from the preceding term x_{n}by multiplying by the factor 1/r, then the sum of all the terms x_{n+1}+ x_{n+2}... is equal to x_{n}* 1/(r-1).

So, I ran a Python simulation and it turns out to be correct!

If I'm reading the article correctly, this turns out to be a simple result from the theory of geometric series, and it looks like it works even for fractional r. Modifying the code above to test fractional r shows this is true. Department of "learn something new every day"....

My guess is that von Neumann saw all three pieces instantly:

**• the first term and step size of the series**

• the formula for the terms after the first one

• the easy way

• the formula for the terms after the first one

• the easy way

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