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I'm interested in understanding the history of the geometric series, especially how it was discovered and whether there exists continued fraction representations for the geometric series, just as there are continued fractions for many elementary functions in mathematics.

I would also appreciate some historical perspective on how geometric series played a role in the development of calculus.

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  • $\begingroup$ You can see the following link The Geometric Series Also you can visit mathcs.slu.edu/history-of-math/index.php/9.2_Geometric_series $\endgroup$ – Sachchidanand Prasad Sep 25 '15 at 9:12
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    $\begingroup$ Apparently, arithmetic/geometric series were already studied in Euclid, though not exactly under this terminology — “continually in proportion”. I don't know (and would like to know) when/where the terminology of arithmetic/geometric series has been invented. $\endgroup$ – ACL Nov 23 '18 at 9:10

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