Talk:Series (mathematics)

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Sum Of Geometric Series[edit]

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 (talkcontribs) 21:07, 31 January 2008 (UTC) 

Properties of Series[edit]

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 (talkcontribs) 10:05, 28 April 2008 (UTC)

Partial sum[edit]

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

Indian Mathematics[edit]

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.


First, the source articles:

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

... 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)


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)


What difference between a "series" and a "sum of a sequence"? What is a "sum of a series"? What difference between the "sum of a sequence" and "sum of a series"? — Preceding unsigned comment added by (talk) 12:27, 15 June 2012 (UTC)

Read the article sequence to see that sums are not required. Further, a sequence may not converge to a limit. Next read partial sum. A sequence does not have a sum, but perhaps has a limit.Rgdboer (talk) 22:33, 18 July 2013 (UTC)

finite infinites[edit]

What about e.g. S = 1 + 10 + 100 + 1000 + ...
Most stupid people will tell you that it is infinity, it diverges, but I think, it is not: it's -1/9 (talk) 01:30, 28 August 2012 (UTC) - Nur weil ich verrückt bin, heißt das noch lange nicht, dass ich deswegen falsch liege.²³

Perhaps you're thinking of something like this? Isheden (talk) 08:29, 18 July 2013 (UTC)
-\sum_{n=1}^\infty \frac{1}{10^n} = -0.111\ldots = -1/9

Open problem?[edit]

I don't see the series

\sum_{n=1}^\infty \frac{1}{n^3}

mentioned in the article. Is it still true that calculating the sum is an open problem? [5] Isheden (talk) 08:36, 18 July 2013 (UTC)

After some time I found a complete article on this sum: Apéry's constant Isheden (talk) 09:23, 19 July 2013 (UTC)

Tag "image requested"[edit]

I have removed the tag "image requested". I think that an image would be a good thing for this article. But, like for many mathematical articles, it is not clear which kind of image would improve the article. Therefore inserting the tag without suggesting the nature of the image that is requested is a non-constructive edit. D.Lazard (talk) 11:38, 20 September 2013 (UTC)


What is the indexed number n called? Is it the "summation variable"? —Kri (talk) 12:38, 18 October 2014 (UTC)

This is not incorrect, but "summation index" is more frequently used. D.Lazard (talk) 14:08, 18 October 2014 (UTC)
Our summation article says says "index of summation". --Mark viking (talk) 16:42, 18 October 2014 (UTC)
Sometimes it is not used as an index, though. Can it stille be referred to as a summation index? E.g. \sum_{n=1}^{N} n^2. —Kri (talk) 15:34, 19 October 2014 (UTC)
Yes, it can be referred to as a "summation index". Be care that in \sum_{n=1}^{N} n^2, n is not really a variable in the sense that it cannot be substituted by a value. It would better be called a "placeholder", as n may be replaced by any symbol without changing the meaning and the value of the expression. Sure that "index" often means subscript, but, in mathematics, it may also mean "discrete variable", as in indexed family. D.Lazard (talk) 16:39, 19 October 2014 (UTC)
Sure it is a variable; it's just a scoped variable and hence cannot be controlled from outside of the series. Hm, I don't know if I would still call it a summation index if it is not actually an index. —Kri (talk) 19:29, 20 October 2014 (UTC)

Indexed by natural numbers or non-negative integers?[edit]

I see the article starts series both at 1 and at 0 without any mention as to why it doesn't matter. If it is indexed by the natural numbers shouldn't start with 1 instead of 0? — Preceding unsigned comment added by (talk) 00:17, 21 July 2015 (UTC)