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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,525

Okay! Thanks.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,695

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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,525

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

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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: 86,695

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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,525

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,695

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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,525

How did you check?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,695

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

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: 15,525

Can you show me what you have done?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,695

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!

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: 15,525

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,695

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

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: 15,525

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,695

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.

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: 15,525

Ok,see you later.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,525

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?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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This is the easiest one:

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

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: 15,525

What did you try?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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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.

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: 15,525

What did they show you?

And what other problem do you have?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,695

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?

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: 15,525

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

Where do you get these problems?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,695

There are several approaches to get the front digit.

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

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: 15,525

Tell me one of the easier approaches.

Who is that guy?

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,525

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)*

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