Talk:Telescoping series

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Not all telescoping sums are infinite series; sum are finite. Should this be moved to telescoping sum? (For a nice example, see the section on probability distributions at order statistic.) Michael Hardy 01:07, 9 Feb 2005 (UTC)

Contents

[edit] Gosper

My recollection is that Bill Gosper introduced the idea of telescoping. He is one of the pioneers of computer symbolic mathematics programs, having contributed to both Macsyma and Mathematica, for example. His web page [1] cites A calculus of Series Rearrangements, which might be the place to look. --KSmrqT 01:52, 3 December 2005 (UTC)

What!!!??? How could he have introduced this idea if his life was so recent that he worked with electronic computers?? Michael Hardy 22:28, 3 December 2005 (UTC)

OK, it is asserted at User talk:KSmrq that the term has been found in a 1957 document on mathscinet. Someone is telling me that it's in a math dictionary published in 1949. More to follow when I get more information. My guess is the term originated between 1850 and 1910 -- but that's just a guess. Telescoping sums were used by Euler in the 18th century, but I suspect not by that name. Michael Hardy 22:46, 5 December 2005 (UTC)

And to be clear, I completely agree that series were being rearranged long before Gosper. One of the challenges of formalization was to understand what rearrangements were safe, as pursued by Karl Weierstrass and others. The questions for this article are, what distinguishes "telescoping", when and where did the term originate, and how is it used today. With respect to current use, Gosper and others have made significant contributions to algorithms used in modern symbolic computer algebra systems, especially with regard to hypergeometric series. In this context the term "creative telescoping" is used. [2] A helpful paper is
  • Abramov et al. "Telescoping in the context of symbolic summation in Maple". Journal of Symbolic Computation, v38 (2004), 1303–1326. (PDF)
The extraordinary generality of hypergeometric series and the power of these modern algorithms [3] [4] [5] allows the discovery of new and valuable identities. See
  • Petkovsek, Wilf, Zeilburger. A=B. (Book available online. [6])
for further details. I apologize if my previous brief remark confused or annoyed the historians! --KSmrqT 22:08, 6 December 2005 (UTC)

[edit] Why use essentially the same example twice?

"Example 1" is essentially the same as the earlier example. Michael Hardy 22:33, 3 December 2005 (UTC)

I propose putting the second occurance first, then putting something like, "This is useful to prove convergence, because as N \rightarrow \infty the sum tends to 1." Then removing that occurance. x42bn6 Talk 07:27, 4 December 2005 (UTC)

[edit] Rewrite

I have found some stuff about this article, and I am rewriting it now at User:x42bn6/Working On/Telescoping series. I would appreciate it if nobody did any major edits to this article, but I welcome feedback at User_talk:x42bn6/Working On/Telescoping series. x42bn6 Talk 13:24, 9 December 2005 (UTC)

[edit] Proof?

Is there a possibility of a proof that relates for telescoping series? By that I mean, is there a formula for finding out what the final value is when it converges? If anyone really wants to talk about it, you can discuss it here. —EdBoy 13:10, 14 August 2006 (UTC)

You may want to ask Wikipedia:Reference Desk/Mathematics but they will probably tell you to do it yourself, using limits. x42bn6 Talk 02:11, 15 August 2006 (UTC)

What the final value is, is certainly stated explicitly in the article. Michael Hardy 21:55, 5 September 2007 (UTC)

[edit] Applications?

I think it would be to include some practical applications of telescoping series in this article, but so far I have not found any. —The preceding unsigned comment was added by Panchaos (talk • contribs) 16:08, 14 March 2007 (UTC).

I've added an application. I think others can be found by clicking on "what links here". Michael Hardy 20:50, 4 September 2007 (UTC)