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**reconsideryouranswer****Member**- Registered: 2011-05-11
- Posts: 172

gAr wrote:

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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

Edit /\/\/\

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

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,462

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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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,462

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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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,462

**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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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,462

**12)**

Show that

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 81,665

Hi gAr;

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

**Online**

**gAr****Member**- Registered: 2011-01-09
- Posts: 3,462

Hi bobbym,

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 81,665

Hi gAr;

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

**Online**

**gAr****Member**- Registered: 2011-01-09
- Posts: 3,462

Hi bobbym,

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

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 81,665

Hi gAr;

Thanks for problem, I enjoyed it.

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

**Online**

**gAr****Member**- Registered: 2011-01-09
- Posts: 3,462

Hi bobbym,

You're welcome.

I too enjoyed that problem!

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,462

**13)**

Evaluate

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,462

Hi,

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 81,665

Hi gAr;

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

**Online**

**gAr****Member**- Registered: 2011-01-09
- Posts: 3,462

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

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,462

Hi bobbym,

Did you know this? http://en.wikipedia.org/wiki/Generating … a_sequence

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 81,665

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?

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

**Online**

**gAr****Member**- Registered: 2011-01-09
- Posts: 3,462

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.

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 81,665

Hi gAr;

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

You can try this with Stirlings formula.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

**Online**

**gAr****Member**- Registered: 2011-01-09
- Posts: 3,462

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".

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 81,665

Okay, see you later.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

**Online**

**gAr****Member**- Registered: 2011-01-09
- Posts: 3,462

Hi bobbym,

First success with that formula!

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 81,665

Hi gAr;

How did you derive that?

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

**Online**

**gAr****Member**- Registered: 2011-01-09
- Posts: 3,462

Hi bobbym,

I have derived the g.f in #113

I'll take a short break.

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 81,665

Hi gAr;

You used that page?

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

**Online**