On this and other Stack Exchange website, there have been question about the so-called geometric series, and where its name comes from. My problem is that most answers follow one of two different ideas.
- Either they show an ingenious, but obviously not ancient, picture that illustrates concrete examples of geometric series summation.
- Or they make some reference to the middle of three consecutive terms in the sequence being the "geometric mean" of the other two.
Well, I want to raise the question again, because neither of these prototype answers really explains where the use of "geometric" started, nor who (if known) came up with it.
Any good explanation?