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#376 2012-04-19 03:30:44

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,521

Re: Series

Okay! Thanks.


“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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#377 2012-04-19 04:02:06

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 86,251

Re: Series

Hi;

I am afraid that I am unable to verify your answer. You will have to wait for 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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#378 2012-04-19 04:03:07

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,521

Re: Series

Ok. But we are talking about my answer to #15?


“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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#379 2012-04-19 04:08:12

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 86,251

Re: Series

It is not your answer but the series itself.


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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#380 2012-04-19 04:09:30

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,521

Re: Series

What is wrong whit the series?


“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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#381 2012-04-19 04:13:37

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 86,251

Re: Series

When x = 1 + (1 /4 ) it is not true. Also for other values too. That does not mean there is something wrong with it as you say. It just means I am not able to verify 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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#382 2012-04-19 04:16:27

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,521

Re: Series

How did you check?


“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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#383 2012-04-19 04:17:23

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 86,251

Re: Series

Numerically, which could be biting me. But that is what I am getting right now.


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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#384 2012-04-19 04:19:41

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,521

Re: Series

Can you show me what you have done?


“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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#385 2012-04-19 04:27:35

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 86,251

Re: Series

For a sum of 10000 terms;

x=N[1+1/4,20];

FullSimplify[Sum[(-1)^k Binomial[2k,k]*(Cos[2k+1]x)/2^(2k),{k,0,10000}]-Cos[x/2]/Sqrt[2Cos[x]]]//N

Answer should be getting close to 0, but it does not. When I do 20000 the answer goes up instead of down!


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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#386 2012-04-19 04:36:08

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,521

Re: Series

I got 0.0284151 and 0.029486 for those two.I will try going larger.


“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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#387 2012-04-19 04:37:38

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,251

Re: Series

As you approach infinity it should be going to 0. But it does not.


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.

Online

#388 2012-04-19 04:47:44

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,521

Re: Series

I don't know. M is slow and it won't calculate anymore. hmm


“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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#389 2012-04-19 04:50:50

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,251

Re: Series

Hi;

Could just be round off error. I got it to work for one value so just submit it to gAr and see if he likes it.

I am going to go shopping 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.

Online

#390 2012-04-19 04:51:39

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,521

Re: Series

Ok,see you later.


“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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#391 2012-04-20 10:53:09

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,521

Re: Series

bobbym wrote:

Sometimes! The ones that you solve in a day or two are fun. But there are those that last for years. Nothing you try works, I have a number of those.

Could you tell me one of them,bobbym?


“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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#392 2012-04-20 10:56:52

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,251

Re: Series

This is the easiest one:

Evaluate the above integral to as many digits as you can. Find a good way to do so.


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.

Online

#393 2012-04-20 11:01:33

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,521

Re: Series

What did you try?


“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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#394 2012-04-20 11:04:53

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,251

Re: Series

Everything I know of course and a few more things. I bounced it around on forums and got a lot of punk answers. Two people did show me something, one was a certain Robert MIller, the other I do not remember. Currently even with a computer and the big boy on the block, I can get only around 100 digits or so easily.


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.

Online

#395 2012-04-20 11:06:44

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,521

Re: Series

What did they show you?

And what other problem do you have?


“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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#396 2012-04-20 11:09:37

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,251

Re: Series

Many others but most of them I cannot recall offhand any longer. I outlined 6 or 7 for gAr when we were talking about this. Oh, here is another:

What is the front digit?


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.

Online

#397 2012-04-20 11:11:07

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,521

Re: Series

How,in the world,would you find the first diigit???

Where do you get these problems?


“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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#398 2012-04-20 11:14:43

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,251

Re: Series

There are several approaches to get the front digit.

Where do I get the problems from? You are familiar with Christian Goldbach?


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.

Online

#399 2012-04-20 11:19:20

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,521

Re: Series

Tell me one of the easier approaches.

Who is that guy?


“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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#400 2012-04-20 11:20:57

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,521

Re: Series

Oooh,Goldbach Theorem Goldbach. Didn't know his first name was Christian.

And look at the last post on the last page,jst in case you miss it.

Last edited by anonimnystefy (2012-04-20 11:22:24)


“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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