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" ! 
March 25th, 2019, 04:20 PM  #3 
Senior Member Joined: Aug 2012 Posts: 2,329 Thanks: 720  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: 540 Thanks: 82 
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  
March 26th, 2019, 08:16 AM  #6  
Newbie Joined: Apr 2015 From: Lima Posts: 21 Thanks: 2  Quote:
 
April 1st, 2019, 03:49 AM  #7  
Senior Member Joined: Jun 2015 From: England Posts: 915 Thanks: 271  Quote:
$\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  
April 8th, 2019, 11:57 AM  #9 
Senior Member Joined: Jun 2015 From: England Posts: 915 Thanks: 271  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 
Newbie Joined: Feb 2019 From: United Kingdom Posts: 27 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.


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