My Math Forum Book about Summation and Product of Sequences

 Math Books Math Book Forum - Math books, ebooks, references

 March 25th, 2019, 12:54 PM #1 Newbie   Joined: Apr 2015 From: Lima Posts: 21 Thanks: 2 Book about Summation and Product of Sequences Hello, I would like to know if there is any book devoted to summations and product of sequences (pi notation). With theory and good exercises.
 March 25th, 2019, 03:11 PM #2 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 This site could PIssibly help: https://math.illinoisstate.edu/day/c...nnotation.html I thought it was "Olé Torero" ! Thanks from idontknow
March 25th, 2019, 04:20 PM   #3
Senior Member

Joined: Aug 2012

Posts: 2,387
Thanks: 746

Quote:
 Originally Posted by JoseTorero Hello, I would like to know if there is any book devoted to summations and product of sequences (pi notation). With theory and good exercises.
Do you mean infinite products? I recall that they're not as interesting as they first seem; because $\log \Pi a_n = \sum \log a_n$ so every infinite product reduces to studying some infinite sum.

 March 25th, 2019, 04:47 PM #4 Senior Member   Joined: Dec 2015 From: somewhere Posts: 637 Thanks: 91 A simple one without infinity : compute $\displaystyle \prod_{n=1}^{m} (-1)^{n}$ . Last edited by idontknow; March 25th, 2019 at 04:53 PM.
March 26th, 2019, 04:51 AM   #5
Newbie

Joined: Apr 2015
From: Lima

Posts: 21
Thanks: 2

Quote:
 Originally Posted by Maschke Do you mean infinite products? I recall that they're not as interesting as they first seem; because $\log \Pi a_n = \sum \log a_n$ so every infinite product reduces to studying some infinite sum.
Yes. Both, infinite sums and infinite products.

March 26th, 2019, 08:16 AM   #6
Newbie

Joined: Apr 2015
From: Lima

Posts: 21
Thanks: 2

Quote:
 Originally Posted by Denis This site could PIssibly help: https://math.illinoisstate.edu/day/c...nnotation.html I thought it was "Olé Torero" !
I think that is only the introduction, there is no further theory, like the telescopic rule, and there are no complex problems.

April 1st, 2019, 03:49 AM   #7
Senior Member

Joined: Jun 2015
From: England

Posts: 915
Thanks: 271

Quote:
 Originally Posted by JoseTorero I think that is only the introduction, there is no further theory, like the telescopic rule, and there are no complex problems.
You are perhaps looking to study things like this?

$\displaystyle \sin \pi \theta = \pi \theta \prod\limits_{n = 1}^\infty {\left( {1 - \frac{{{\theta ^2}}}{{{n^2}}}} \right)}$

Last edited by studiot; April 1st, 2019 at 03:55 AM.

April 8th, 2019, 11:43 AM   #8
Newbie

Joined: Apr 2015
From: Lima

Posts: 21
Thanks: 2

Quote:
 Originally Posted by studiot You are perhaps looking to study things like this? $\displaystyle \sin \pi \theta = \pi \theta \prod\limits_{n = 1}^\infty {\left( {1 - \frac{{{\theta ^2}}}{{{n^2}}}} \right)}$
More or less

April 8th, 2019, 11:57 AM   #9
Senior Member

Joined: Jun 2015
From: England

Posts: 915
Thanks: 271

Quote:
 Originally Posted by JoseTorero More or less
I posted a week ago and have forgotten about it since.
I think that example came from Archbold, but I would have to look it up again.
I seem to remember that professor Fort wrote about these in a book on sequences and series, I will try to dig that one out.

 April 8th, 2019, 03:11 PM #10 Member     Joined: Feb 2019 From: United Kingdom Posts: 44 Thanks: 3 It wouldn't make any sense to devote a whole book to sum and product sequences. Even if you did, you'll just be repeating what's been said before.

 Tags book, product, sequences, summation

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post DATAfiend Pre-Calculus 6 November 16th, 2014 06:08 PM eddybob123 Number Theory 3 May 13th, 2013 03:48 PM annakar Real Analysis 0 December 9th, 2012 01:04 AM jmu123 Real Analysis 3 December 8th, 2010 04:40 PM dagitt Calculus 6 May 30th, 2009 01:52 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top