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#101 2011-08-05 17:21:26

reconsideryouranswer
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Registered: 2011-05-11
Posts: 172

Re: Series

gAr wrote:

Unhide:

Did you observe anything by plugging in some large values for n?

I don't see (as in I am not seeing it at this moment) what your hint will do.


When k catches up to n, then I see the 'last' term as









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Last edited by reconsideryouranswer (2011-08-05 17:35:32)


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#102 2011-08-05 17:24:08

gAr
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Registered: 2011-01-09
Posts: 3,479

Re: Series

Oh, okay!

The teachers usually teach the way they were taught. And if they never used computers before, it is likely that they wouldn't use it in the future!


"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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#103 2011-08-05 17:29:06

gAr
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Registered: 2011-01-09
Posts: 3,479

Re: Series

reconsideryouranswer wrote:

I don't see (as in I am not seeing it at this moment) what your hint will do.


When k catches up to n, then I see the 'last' term as



You only saw what the last term was, but didn't see what happens on summation.


"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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#104 2011-08-06 21:13:22

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Series

11)

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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#105 2011-08-06 23:32:32

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Series

12)

Show 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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#106 2011-08-07 00:28:17

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,776

Re: Series

Hi gAr;


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#107 2011-08-07 00:40:02

gAr
Member
Registered: 2011-01-09
Posts: 3,479

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."

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#108 2011-08-07 00:43:40

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,776

Re: Series

Hi gAr;


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#109 2011-08-07 00:47:03

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Series

Hi bobbym,

No problem. It's just a minor, aesthetic thing!


"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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#110 2011-08-07 00:51:04

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,776

Re: Series

Hi gAr;

Thanks for problem, I enjoyed it.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#111 2011-08-07 00:57:48

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Series

Hi bobbym,

You're welcome.
I too enjoyed that problem!


"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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#112 2011-08-07 04:22:29

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Series

13)


Evaluate


"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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#113 2011-08-10 02:28:43

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Series

Hi,



"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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#114 2011-08-10 03:14:11

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,776

Re: Series

Hi gAr;


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#115 2011-08-10 03:27:10

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Series

Last edited by gAr (2011-08-10 04:42:10)


"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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#116 2011-08-10 05:46:32

gAr
Member
Registered: 2011-01-09
Posts: 3,479

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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#117 2011-08-10 05:49:46

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,776

Re: Series

Hi gAr;

Yes, I have been there. I have never been able to get one of those to work. Do you have an idea?

I trust you mean the asymptotic forms?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#118 2011-08-10 05:57:23

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Series

Yes, asymptotics.

Okay, I just saw it now.
I don't have much idea either. Even if I manage to get an asymptotic form, I don't know how to verify.


"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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#119 2011-08-10 06:01:09

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,776

Re: Series

Hi gAr;

I think the ratio of the f(n) and its asymptotic form  g(n) is

You can try this with Stirlings formula.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#120 2011-08-10 06:08:20

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Series

Okay, thanks.
I'll try for the g.f's which we had done earlier.

I'm taking a break to sleep. See you "tomorrow".


"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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#121 2011-08-10 06:09:02

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,776

Re: Series

Okay, see you later.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#122 2011-08-10 18:00:14

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Series

Hi bobbym,

First success with that formula!


"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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#123 2011-08-10 20:04:24

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,776

Re: Series

Hi gAr;

How did you derive that?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#124 2011-08-10 20:15:52

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Series

Hi bobbym,

I have derived the g.f in #113


I'll take a short break.


"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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#125 2011-08-10 20:18:32

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,776

Re: Series

Hi gAr;

You used that page?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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