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#1 2011-07-30 23:13:40
- gAr
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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."
#2 2011-07-31 02:04:39
- bobbym
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Re: Series
Hi gAr;
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#3 2011-07-31 02:14:49
- 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."
#4 2011-07-31 02:19:08
- bobbym
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Re: Series
Hi gAr;
I know but I could not resist.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#5 2011-07-31 02:28:02
- gAr
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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."
#6 2011-07-31 02:45:37
- bobbym
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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.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#7 2011-07-31 02:50:05
- gAr
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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."
#8 2011-07-31 14:59:50
- bobbym
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Re: Series
Hi gAr;
Nothing yet, just some dead ends.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#9 2011-07-31 15:15:27
- gAr
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Re: Series
Hi bobbym,
Okay,
a
Last edited by gAr (2011-07-31 15:23:58)
"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."
#10 2011-07-31 15:19:58
- bobbym
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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.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#11 2011-07-31 15:22:32
- gAr
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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."
#12 2011-07-31 19:55:10
- bobbym
- Administrator
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Re: Series
Hi gAr;
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#13 2011-07-31 20:30:57
- gAr
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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."
#14 2011-07-31 20:38:22
- bobbym
- Administrator
Online
Re: Series
Hi gAr;
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#15 2011-07-31 20:48:57
- gAr
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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."
#16 2011-07-31 21:00:03
- bobbym
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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.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#17 2011-07-31 21:07:34
- gAr
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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."
#18 2011-07-31 21:10:59
- bobbym
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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.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#19 2011-07-31 21:16:46
- gAr
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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."
#20 2011-07-31 21:33:12
- bobbym
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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.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#21 2011-07-31 21:36:31
- gAr
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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."
#22 2011-07-31 22:15:04
- bobbym
- Administrator
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Re: Series
Hi gAr;
No problem, do not worry about it.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#23 2011-07-31 23:18:23
- gAr
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Re: Series
3)
Find
Last edited by gAr (2011-08-26 20:48:55)
"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."
#24 2011-08-01 15:45:15
- gAr
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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."
#25 2011-08-01 20:21:16
- bobbym
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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.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.