alt Hacker NewsAny function that infinitely slowly converges to a finite number will have this property. Discretely, think of 1/2 + 1/4 + 1/8 and so on. The sequence goes on forever but adds up to 1.
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almostgotcaught • today at 4:45 AM
I have no idea why you think the geometric series has anything to do with this - this is related to continuous but nowhere differentiable functions: https://en.wikipedia.org/wiki/Weierstrass_function
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A continuous function with that property is f(x) := 2^-x (when summed over the non-negative part of the x-axis). Another example is g(x) := 1/x^2.