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## #26 2011-08-07 02:11:41

gAr
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### Re: Sequences!

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."

## #27 2011-08-14 07:52:35

anonimnystefy
Real Member

Online

### Re: Sequences!

hi gAr

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

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

## #28 2011-08-26 04:51:02

anonimnystefy
Real Member

Online

### Re: Sequences!

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

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

## #29 2011-08-26 19:01:03

bobbym

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### Re: Sequences!

Hi;

Generating functions are the creators of the sequences.

In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

## #30 2011-08-26 23:09:47

anonimnystefy
Real Member

Online

### Re: Sequences!

how can you be so sure?

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

## #31 2011-08-27 03:07:09

bobbym

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### Re: Sequences!

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.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

## #32 2011-08-27 03:08:57

anonimnystefy
Real Member

Online

### Re: Sequences!

i find finding taylor and maclaurin series very amusing.

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

## #33 2011-08-27 03:21:20

bobbym

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### Re: Sequences!

Amusing or confusing?

In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

## #34 2011-08-27 03:44:12

anonimnystefy
Real Member

Online

### Re: Sequences!

amusing as u can see!

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

## #35 2011-08-27 03:48:55

bobbym

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### Re: Sequences!

Hi anonimnystefy;

Then you understand them! Very good!

In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

## #36 2011-08-27 05:12:19

anonimnystefy
Real Member

Online

### Re: Sequences!

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.

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

## #37 2011-08-27 05:43:41

bobbym

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### Re: Sequences!

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?

In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

## #38 2011-08-27 05:49:24

anonimnystefy
Real Member

Online

### Re: Sequences!

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.

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

## #39 2011-08-27 05:52:16

bobbym

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### Re: Sequences!

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?

In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

## #40 2011-08-27 05:55:13

anonimnystefy
Real Member

Online

### Re: Sequences!

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'.

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

## #41 2011-08-27 05:59:46

bobbym

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### Re: Sequences!

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.

In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

## #42 2011-08-27 06:07:05

anonimnystefy
Real Member

Online

### Re: Sequences!

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.

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

## #43 2011-08-27 06:24:56

bobbym

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### Re: Sequences!

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

In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

## #44 2011-08-27 08:06:29

anonimnystefy
Real Member

Online

### Re: Sequences!

that i know.

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

## #45 2011-08-27 08:10:32

bobbym

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### Re: Sequences!

Yes, but do you know what that really means?

And why were they so interested in Taylor series anyway?

In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

## #46 2011-08-27 08:31:58

LQ
Real Member

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### Re: Sequences!

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...

## #47 2011-08-27 08:38:20

bobbym

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### Re: Sequences!

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.

In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

## #48 2011-08-27 08:42:47

LQ
Real Member

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### Re: Sequences!

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...

## #49 2011-08-27 20:16:59

anonimnystefy
Real Member

Online

### Re: Sequences!

hi LQ

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

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

## #50 2011-08-28 18:33:20

moon1
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### Re: Sequences!

Can any one hep me to find the solution for this
4, 5, 12, 39, 114, 226, 225, ----,-----, -----