FWIW:

Definition of geometric series

[QUOTE]First Known Use: circa 1909
[/QUOTE]

[url]https://www.merriam-webster.com/dictionary/geometric%20series[/url]


series
[QUOTE]First Known Use: 1611[/QUOTE]

[url]https://www.merriam-webster.com/dictionary/series[/url]

[QUOTE=a1call;463648]FWIW:

Definition of geometric series



[url]https://www.merriam-webster.com/dictionary/geometric%20series[/url]


series


[url]https://www.merriam-webster.com/dictionary/series[/url][/QUOTE]

there are many types of series so what's the point ? there are infinite series, finite series, convergent series, divergent series, formal power series, power series, geometric series, arithmetic series, harmonic series, basically if there's a type of sequence, you can turn it into a type of series. This list also forgets special kinds like Taylor series, Maclaurin series, etc. Edit:

[QUOTE="http://jeff560.tripod.com/g.html"]GEOMETRIC SERIES is found in 1723 in A System of the Mathematics James Hodgson [Google print search, James A. Landau].[/QUOTE] though it may be in a different definition who knows.

[B][SIZE=3]Webster's Dictionary 1828 - Online Edition[/SIZE][/B]



[QUOTE][B]Series[/B]



...

[B]4.[/B] In [I]arithmetic[/I] and [I]algebra[/I], a number of terms in succession, increasing or diminishing in a certain ratio; as arithmetical [I]series[/I] and geometrical [I]series[/I]. [See [I]Progression[/I].]
[/QUOTE]

In 1913:

[QUOTE][B]3.[/B] [I](Math.)[/I] An indefinite number of terms succeeding one another, each of which is derived from one or more of the preceding by a fixed law, called the [I]law[/I] of the series; as, an arithmetical [I]series[/I]; a geometrical [I]series[/I].
[/QUOTE]



[url]http://www.websters1913.com/words/Series[/url]

[QUOTE=a1call;463650][B][SIZE=3]Webster's Dictionary 1828 - Online Edition[/SIZE][/B]





In 1913:





[url]http://www.websters1913.com/words/Series[/url][/QUOTE]

okay, well I believe these sequences of numbers, are usually the easiest nowadays to find the value of the sum, if they fit within certain rules. [TEX]a\over1-r[/TEX] a being teh starting term and r being the ratio for a geometric sequence being summed as long as this is not greater in absolute value than 1.

Websters Definitions in 1943 are attached.

[QUOTE=a1call;463653]Websters Definitions in 1943 are attached.[/QUOTE]

I agree see Succession. in theory succession could be adding.