Talk:Geometric series

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geometric power series application?[edit]

In the article's "Coefficient a" section, I describe the relationship between the geometric series and the power series. In the article's "Applications" section, there is a "geometric power series" application. Is there a reference for a series named the "geometric power series"? Gj7 (talk) 20:51, 26 December 2020 (UTC)Reply[reply]

The comments about differentiating the geometric series have been moved to the Historic insights section on Nicole Oresme. Therefore, all that remains is a description of Gregory's series. In my opinion, there should also be a Historic insights section on Madhava of Sangamagrama and this description of Gregory's series should then be moved there (and the "geometric power series" subsection should then be deleted). Gj7 (talk) 21:49, 7 June 2021 (UTC)Reply[reply]
I finally changed this heading name from "geometric power series" to "integration" and I attributed the resulting series to Madhava of Sangamagrama. Gj7 (talk) 17:31, 4 June 2022 (UTC)Reply[reply]

Original research?[edit]

Last year after reading Thousand Brains - a new theory of intelligence by Jeff Hawkins, I started to think about the importance of a useful mental model when learning math. As described in A Thousand Brains, being actionable and simple and hierarchical are characteristics of a useful mental model. Intending to help high school math students, I posted an image of a map of polynomials with the geometric series at the origin, showing the relative locations of the power series, the Laurent series, and matrix polynomials ... all of which are covered in their own Wikipedia articles.

Today, an anonymous editor removed that map of polynomials and claimed it is original research. Can an image that shows a particular organization of existing content be original research? If so, it seems that most images in Wikipedia articles would also be original research (e.g., during the image upload process there is a checkbox to verify that the person uploading the image is also the image creator). Gj7 (talk) 23:03, 25 July 2022 (UTC)Reply[reply]

I agree with the anonymous editor. This appears to be original research, only dubiously relevant to the topic, overly promotional for the book, and not sourced by reliable publications in the mathematics literature. I don't think it belongs in this article. —David Eppstein (talk) 23:24, 25 July 2022 (UTC)Reply[reply]
The quotes from the book were not intended as a promotion, but as a reference about the task of finding an actionable, simple, and hierarchical mental model is a key to gaining expertise in anything, including math. Why would the geometric series being at the origin of the image be only dubiously relevant to the topic? Do you know of a different and better mental model of math that illustrates the relationship between different series? — Preceding unsigned comment added by Gj7 (talkcontribs) 23:49, 25 July 2022 (UTC)Reply[reply]

Mistake in section "Repeating decimals"[edit]

The statement "In fact, any fraction that has an infinitely repeated pattern in base-ten numbers also has an infinitely repeated pattern in numbers written in any other base." is fundamentally wrong.

Infinitely repeating patterns occur when dividing by such a number, which contains a prime factor, that is not part of the base of the number system. That means, finite sequences will occur only for a limited number of divisors (in base 10 only for the primes 2 and 5 (and these powers and combinations; in base 2 only for the prime 2 and its powers). Division by any other primes (or their powers and combinations) will result in infinitely repeating patterns.

The example for 0.777... (which is equal to 7/9) used base 2, where it is also an infinitely repeating binary number, but this is no proof. It is only because base 2 does not include the prime number 3, which is the prime number included in the division (7/3^2). If you consider the same in base 3, 7/9 is written as 0.21, or in base 9 it is 0.7. It will be represented in finite length also in base 12 for example, 0.91 would be the representation. 2001:4C4E:10FE:8A00:5803:4BB7:58AC:9406 (talk) 11:20, 28 October 2022 (UTC)Reply[reply]

There is an infinitely repeating pattern of zeros following any finite-length representation. These numbers in fact have two infinitely repeating representations, one with an infinitely repeating pattern of zeros and another with an infinitely repeating pattern of the base minus one. —David Eppstein (talk) 15:38, 28 October 2022 (UTC)Reply[reply]

Correction for topic 'Mistake in section "Repeating decimals"'[edit]

The representation of 7/9 in base 12 is 0.94 (and NOT 0.91). Sorry for the typo, I could not change it after publishing my comment. 2001:4C4E:10FE:8A00:5803:4BB7:58AC:9406 (talk) 11:34, 28 October 2022 (UTC)Reply[reply]

Opening sentence is confusing.[edit]

"In mathematics, a geometric series is the sum of an infinite number of terms that have a constant ratio between successive terms." We can't sum an infinite number of terms. This needs to be broken down along the lines as follows: "Each term of a geometric series is the sum of a finite number of terms of a geometric sequence" or similar. TorlachRush (talk) 19:50, 12 April 2023 (UTC)Reply[reply]