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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,606

Okay! Thanks.

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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: 89,002

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.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,606

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 89,002

It is not your answer but the series itself.

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,606

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: 89,002

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.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,606

How did you check?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 89,002

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.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,606

Can you show me what you have done?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 89,002

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.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,606

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: 89,002

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.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,606

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: 89,002

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.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,606

Ok,see you later.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,606

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
- Posts: 89,002

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.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,606

What did you try?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 89,002

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.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,606

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: 89,002

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.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,606

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: 89,002

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.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,606

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: 15,606

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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