Talk:Series (mathematics)

Sum Of Geometric Series

I have taken this from a math textbook, but i dont want to post it until i find the copyright information, can someone confirm that this is correct?

"The sum of a finite geometric series is $\sum_{n=1}^b ar^{n-1}.$. If this finite sum S of n approaches a number L as n to infinity, the series is said to be convergent and converges to L and L is the sum of the infinite geometric series.

Thm: Sum of an Infinite Geometric Series:

    If the absolute value of r is less than one, the sum of the infinite geometric series $\sum_{n=1}^\infty ar^{n-1}.$ is $\frac{a}{1-r}$  —Preceding unsigned comment added by Dandiggs (talk • contribs) 21:07, 31 January 2008 (UTC) 

Properties of Series

I think that there should be a section on the properties of series, such as multipication of series and commutativity of multiplied series. Lore aura (talk) 10:07, 28 April 2008 (UTyC) —Preceding unsigned comment added by Lore aura (talk • contribs) 10:05, 28 April 2008 (UTC)

Partial sum

What is a partial sum? Partial sum is a redirect to this page, even though it is linked to from various other math pages. There is no partial sum subsection in this article. --Cryptic C62 · Talk 02:24, 25 May 2008 (UTC)

In response to this question, I've improved the definition and rejigged the first bit of the page. Still needs a lot of work though! SetaLyas (talk) 02:00, 29 December 2008 (UTC)

Yea, I still have no idea what a partial sum is. McBrayn (talk) 15:10, 16 April 2009 (UTC)

From the article:

Basic properties

Given an infinite sequence of real numbers {a_n}, define

$S_N =\sum_{n=0}^N a_n=a_0+a_1+a_2+\cdots+a_N.$

Call S_N the partial sum to N of the sequence {a_n}, or partial sum of the series.

What more should one say? --Bdmy (talk) 21:36, 16 April 2009 (UTC)

Remainder

Remainder term redirects here but there is no introduction to the concept of remainder in infinite series on this page. --209.4.252.99 (talk) 19:24, 5 May 2009 (UTC)

Indian Mathematics

The section on Kerala needs to be rewritten as it incorrectly implies that the Kerala school made a significant contribution that was built upon by others and worse implies that Gregory used this work.Xp fun (talk) 21:01, 15 August 2009 (UTC)

Can you tell us more accurately what happened? JamesBWatson (talk) 09:55, 20 August 2009 (UTC)

I'll try, there is a systematic list of articles which have been modified some time ago to include claims that this Kerala school had invented the technique or concept centuries before the generally accepted mathematicians or physicists.

The idea behind this is in a couple of books cited in each article which alleges (not having read the book) that Madhava on the Kerala school (or his disciples) had discovered these ideas and through trade and commerce the ideas came to western mathematicians.

Now there are several websites which site these same couple of books, and these websites are used as additional links in citations creating a circular web of authority. Anyone reading any of these updates would probably check the links, see that they appear to research actual texts, and stop there. Only digging deeper do we see that there is no further original research than the first author.

Evidence

First, the source articles:

• Madhava_of_Sangamagrama
• Template:Kerala school of astronomy and mathematics

Articles potentially tainted (Found via search of "madhava or Kerala")

• Leibniz formula for pi (redirect from Madhava-Leibniz)
• Integral test for convergence
• History of geometry
• History of calculus
• History of mathematics
• Numerical approximations of π
• Calculus
• Science in the Middle Ages
• Irrational number
• Timeline of mathematics
• Series (mathematics)
• History of astronomy (Possibly)
• Taylor series
• List of important publications in mathematics
• Mathematical analysis
• History of science
• James Gregory (mathematician) (how is Madhava even remotely relevant in this article?)
• History of trigonometry
• Mean_value_theorem

... the list goes on, more exhaustive search will be required. List of supplied references

Cited Article	Comment	Citation
Mathematical_analysis#cite_ref-4	Madhava of Sangamagrama, regarded by some as the "founder of mathematical analysis".	G. G. Joseph (1991). The crest of the peacock, London
History_of_science#cite_ref-15	In particular, Madhava of Sangamagrama is considered the "founder of mathematical analysis"	George G. Joseph (1991). The crest of the peacock. London.
History_of_trigonometry#cite_ref-19		O'Connor and Robertson (2000)
History_of_trigonometry#cite_ref-20		Pearce (2002)
James_Gregory_(mathematician)	Under See also is a link "Possible transmission of Kerala mathematics to Europe" "In 1671, or perhaps earlier, he rediscovered the theorem that 14th century Indian mathematician..."	no citations at all
Mean_value_theorem#cite_ref-1	probably least biased reference I've found so far	J. J. O'Connor and E. F. Robertson (2000). [[1]]

Ok, lets take that last one: O'Connor and Robertson. Actually, the site is a mirror of the MacTutor archive located at [[2]]

From there is a link to the interesting biography of Madhava [[3]]

And from there is the list of references: [[4]]

And Finally: at the top of the list: G G Joseph, The crest of the peacock (London, 1991)

I'm not disputing whether or not Madhava and his disciples did interesting things with geometry, nor whether the Mayan, Egyptian, or Native plains people of the Americas, had also discovered fascinating relations in nature. I'm objecting to the idea that this has had any relevance to the furthering of knowledge by the currently aknowledged authors of these ideas. Am I nuts here or are we witnessing an overzealous patriot trying to boost his/her country's esteem?Xp fun (talk) 18:16, 4 September 2009 (UTC)

Notation

Hi. Would it be possible at the beginning of the article to explain the sigma notation? I.e. what the small figures at the top and bottom of the sigma represent? I think that an introductory textbook would do this, and it would be helpful to many maths learners. Thanks for considering it. Itsmejudith (talk) 18:17, 11 November 2009 (UTC)