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March 25th, 2019, 12:54 PM   #1
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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.
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March 25th, 2019, 03:11 PM   #2
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This site could PIssibly help:
https://math.illinoisstate.edu/day/c...nnotation.html

I thought it was "Olé Torero" !
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March 25th, 2019, 04:20 PM   #3
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Quote:
Originally Posted by JoseTorero View Post
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.
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March 25th, 2019, 04:47 PM   #4
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A simple one without infinity : compute $\displaystyle \prod_{n=1}^{m} (-1)^{n}$ .

Last edited by idontknow; March 25th, 2019 at 04:53 PM.
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March 26th, 2019, 04:51 AM   #5
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Originally Posted by Maschke View Post
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.
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March 26th, 2019, 08:16 AM   #6
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Originally Posted by Denis View Post
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.
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April 1st, 2019, 03:49 AM   #7
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Originally Posted by JoseTorero View Post
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.
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April 8th, 2019, 11:43 AM   #8
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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
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April 8th, 2019, 11:57 AM   #9
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Originally Posted by JoseTorero View Post
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.
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April 8th, 2019, 03:11 PM   #10
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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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