Not really going anywhere. Just sitting on my balcony, exercising my mind.:smile:

It's odd no one seems to have contemplated the concept of power-of-series before.

[QUOTE=a1call;463484]Not really going anywhere. Just sitting on my balcony, exercising my mind.:smile:

It's odd no one seems to have contemplated the concept of power-of-series before.[/QUOTE]

the result would depend on if they were finite or infinite etc.

That is the case with all series operations including sum and product. That's no reason for such a concept not to exist.

[QUOTE=a1call;463486]That is the case with all series operations including sum and product. That's no reason for such a concept not to exist.[/QUOTE]

sorry I'm probably confusing you I was thinking arithmetic progressions etc. but a series is a sum. so what is the product of two sums ? and I think you might look up the multinomial theorem.

A series is a number of progressive terms (finite or else).
The sum-of-series is the sum of the terms.
The product-of-series is the product of the terms.
The power-of-series would be the power of first term to power of the second term....
There is a similar concept named tower, but not quite the same thing.

[QUOTE=a1call;463488]A series is a number of progressive terms (finite or else).
The sum-of-series is the sum of the terms.
The product-of-series is the product of the terms.
The power-of-series would be the power of first term to power of the second term....
There is a similar concept named tower, but not quite the same thing.[/QUOTE]

technically a [URL="https://en.wikipedia.org/wiki/Series_(mathematics)"]series[/URL] is a sum of terms.

[QUOTE=science_man_88;463489]technically a [URL="https://en.wikipedia.org/wiki/Series_(mathematics)"]series[/URL] is a sum of terms.[/QUOTE]
Thank you for the clarification. I find that definition illogical.
I suspect it is a relatively recent definition for the word, hence the inclusion of the term "roughly" in that article.

[QUOTE=a1call;463490]Thank you for the clarification. I find that definition illogical.
I suspect it is a relatively recent definition for the word, hence the inclusion of the term "roughly" in that article.[/QUOTE]

I think roughly is to simplify the technical meaning. Taylor series for example, go back to a mathematician from the late 1600's early 1700's.

Here they distinguish the term series and sequence, which to me are synonimous.
Note the conflicting title:

[url]https://www.varsitytutors.com/hotmath/hotmath_help/topics/sum-of-the-first-n-terms-of-a-series[/url]


[url]http://www.google.com/search?q=sequence+synonimous[/url]

[QUOTE]se·quence
ˈsēkwəns/
noun
1.
a particular order in which related events, movements, or things follow each other.
synonyms: succession, order, course, [B]series[/B], chain, train, string, progression, chronology, timeline; More[/QUOTE]

[QUOTE=a1call;463492][url]http://www.google.com/search?q=sequence+synonimous[/url][/QUOTE]

[QUOTE][B]MATHEMATICS[/B]
an infinite ordered series of numerical quantities.[/QUOTE]

so series is sometimes used to describe it even in math . meaning is always context dependent.

[url]http://www.purplemath.com/modules/series.htm[/url] may help you.

Sequence is 1,2,3,...; series is 1+2+3+....