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

Yes, it can't have a general term!

and I didn't understand #24 ?

"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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

hi gAr

it was an answer to bobbym's question but with a sidecomment...

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

hi guys

in the other post g.f.s were mentioned,so i remembered this topic.

bobbym,

you were right this did turn to the g.f.s

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,366

Hi;

Generating functions are the creators of the sequences.

**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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

how can you be so sure?

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,366

If you read generatingfunctionology then you should be a little bit conversant with the concept.

Everything starts with the Taylor and Mclaurin series. If you consider that the series with each x^n being just a place holder and the coefficients are the sequence. Herbie calls it a clothesline and that term has stuck.

**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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

i find finding taylor and maclaurin series very amusing.

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,366

Amusing or confusing?

**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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

amusing as u can see!

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,366

Hi anonimnystefy;

Then you understand them! Very good!

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

yes but i haven't done many.that's where your help part comes in.

i know how to find e.i. the Maclaurin series for sine,cosine,exp functions,but not for tangent,cotangent,sin(x)e^x,etc.

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,366

Hi;

Doing some of those would not be easy at all. Why not just look them up? Must you build the plane to fly to London?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

hi

bobbym wrote:

Must you build a plane to fly to London

Not if your goal is to fly to London.but if your goal is to build a plane that can fly to london,now that's a different thing.and there's no math in there.

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,366

Some things you just do a few times and after that you let technology handle it. For instance;

817265341651718 * 1827653647591 = ?

9188275999917625431093 / 9821625142673 = ?

√(71627263514889000726152) = ?

Do you want to do them?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

hi

i do not want to do them because that is not my goal.but once i started calculating 2^64 with the help of my friend,because that was my 'goal'.

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,366

Everybody does that once in their life. I once did the calculation for 500 light years in terms of miles.

But that is the point, you do it once after that you let a calculator do it. If you know how to differentiate and can plug into a formula than you can do a Taylor series. it is much more important to be able to use them. To know what they do.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

u see i like it when i ask someone to give me a number and then i take a square root of it by hand.

i actually don't know what ts and mcs can be used for.that's why i seek your enlightenment.

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,366

A Taylor series in its most basic form is an attempt to approximate some function by a really big polynomial.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

that i know.

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,366

Yes, but do you know what that really means?

And why were they so interested in Taylor series anyway?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**LQ****Real Member**- Registered: 2006-12-04
- Posts: 1,281

I love them. the approximation proving is intense, it's like love.

I see clearly now, the universe have the black dots, Thus I am on my way of inventing this remedy...

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,366

That is actually the secondary by far aspect of them. They were created to compute things. Numbers! Fact is we know everything about polynomials and little about any non - linear function. It is only natural to want to represent everything in terms of polynomials. Your calculator, computer and all the guys used them for precisely that purpose. The whole field of numerical analysis is really nothing more than a study of taylor series.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**LQ****Real Member**- Registered: 2006-12-04
- Posts: 1,281

You know the value sin(x)=0 then you derivate both sides and get sin(x) = p. then you just derivate on and on...

After that you integrate back each and every one of those derivates and you get a serie. That serie can save lifes, I'm telling you!

I see clearly now, the universe have the black dots, Thus I am on my way of inventing this remedy...

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

hi LQ

how does the derivative of sine equal to sine,and the derivative of 0 equal p?

Here lies the reader who will never open this book. He is forever dead.

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**moon1****Member**- Registered: 2011-08-27
- Posts: 1

Can any one hep me to find the solution for this

4, 5, 12, 39, 114, 226, 225, ----,-----, -----

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