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#1 2011-07-30 01:13:40
- gAr
- Member
- Registered: 2011-01-09
- Posts: 3,482
Series
Problems on partial / infinite series.
Prove that
1)
2)
Deduce that
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
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#2 2011-07-30 04:04:39
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Series
Hi gAr;
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#3 2011-07-30 04:14:49
- gAr
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Re: Series
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
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#4 2011-07-30 04:19:08
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Series
Hi gAr;
I know but I could not resist.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#5 2011-07-30 04:28:02
- gAr
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- Registered: 2011-01-09
- Posts: 3,482
Re: Series
Okay!
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
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#6 2011-07-30 04:45:37
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Series
Hi gAr;
Working on it the right way now, will post the answer if I get it.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#7 2011-07-30 04:50:05
- gAr
- Member
- Registered: 2011-01-09
- Posts: 3,482
Re: Series
Hi,
Okay, take your time.
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
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#8 2011-07-30 16:59:50
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Series
Hi gAr;
Nothing yet, just some dead ends.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#9 2011-07-30 17:15:27
- gAr
- Member
- Registered: 2011-01-09
- Posts: 3,482
Re: Series
Hi bobbym,
Okay,
a
Last edited by gAr (2011-07-30 17:23:58)
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
Offline
#10 2011-07-30 17:19:58
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Series
Hi gAr;
I do not need the hint yet, have a couple of ideas left. Taking a break to rest. See you them.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
Offline
#11 2011-07-30 17:22:32
- gAr
- Member
- Registered: 2011-01-09
- Posts: 3,482
Re: Series
Okay, see you later.
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
Offline
#12 2011-07-30 21:55:10
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Series
Hi gAr;
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
Offline
#13 2011-07-30 22:30:57
- gAr
- Member
- Registered: 2011-01-09
- Posts: 3,482
Re: Series
Hi bobbym,
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
Offline
#14 2011-07-30 22:38:22
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Series
Hi gAr;
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#15 2011-07-30 22:48:57
- gAr
- Member
- Registered: 2011-01-09
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Re: Series
Okay.
I was confused by W|A's output!
Isn't that always 0?
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
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#16 2011-07-30 23:00:03
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Series
Hi gAr;
I do not think so. I solved for it as a definite integral:
integrate(log(2*cos(x/2))cos(n*x),{x,-Pi,Pi})/Pi
I just plugged in n = 0, 1, 2, 3, 4, 5
That works at home but Alpha is dogging it.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#17 2011-07-30 23:07:34
- gAr
- Member
- Registered: 2011-01-09
- Posts: 3,482
Re: Series
Hi,
Okay.
Could you deduce the sum?
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
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#18 2011-07-30 23:10:59
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Series
Hi;
To get a feel for the coeficients:
nintegrate(log(2*cos(x/2))*cos(n*x),{x,-Pi,Pi})/Pi
Substitute for n =0,1,2,3,4,5 one at a time.
Could you deduce the sum?
If I have to use 1), so far I do not have any idea how to do it.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#19 2011-07-30 23:16:46
- gAr
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- Registered: 2011-01-09
- Posts: 3,482
Re: Series
I have confirmed the coefficients.
In sage, numerical integral is okay, but integral shows 0. Even the sum, for some n, it goes completely wrong!
Do you need a hint or will you try some more time?
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
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#20 2011-07-30 23:33:12
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Series
Hi gAr;
A hint? I need a doctor! I will try to do it as soon as I finish eating and take a little break.
Thanks for posing the problem.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#21 2011-07-30 23:36:31
- gAr
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- Registered: 2011-01-09
- Posts: 3,482
Re: Series
Hi bobbym,
Okay, see you later.
I think I sounded like I was in a hurry, sorry.
You're welcome!
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
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#22 2011-07-31 00:15:04
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Series
Hi gAr;
No problem, do not worry about it.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#23 2011-07-31 01:18:23
- gAr
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- Registered: 2011-01-09
- Posts: 3,482
Re: Series
3)
Find
Last edited by gAr (2011-08-25 22:48:55)
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
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#24 2011-07-31 17:45:15
- gAr
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- Registered: 2011-01-09
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Re: Series
4)
This appeared in AMM
Find
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
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#25 2011-07-31 22:21:16
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Series
Hi;
I have been unable to deduce:
from
Did you have a solution?
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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