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- Value of $\sum\limits_n x^n$ 5 answers
Assume that I have 1 unit of something and then I add ½ unit resulting in a total of 1.5 units. Then I add half of the half (0.25 units) for a total of 1.75 units. Then I add the half of the half of the half (0.125 units) resulting in 1.875 units. IIUC, the result will be finite and have a limit but what is it and is there a general formula I'm looking for?
The problem seems similar to a Riemann sum where an infinite sequence has a finite value, or similar to Xeno's paradox about Achilles and the tortoise.