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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,607

44721 terms?

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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: 89,048

I do not think that is enough.

**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: 15,607

Are you 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: 89,048

To achieve 10 places of accuracy we need an error less than .000 000 000 05

We solve the equation:

**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: 15,607

That is exactly what I did. I got 44722.359... Which rounds up to 44723. That is the beginning of the tail so we are taking one term less which is 44722.

I see also that I posted 44721. Whoops...

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: 89,048

Hi;

When I solve it I got n = 141421.356

**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: 15,607

Could you show me your steps?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 89,048

Times both sides by n^2.

**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: 15,607

I see where my mistake is-I somehow got 2 with 9 zeros in it. Ok,so how would you accelerate this sequence?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 89,048

There are many ways but we are doing the RRA.

**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: 15,607

I know we are doing RRA,but what is the method RRA uses?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 89,048

Nothing but simple algebra. I will do one more and then we will look at how it works.

**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: 15,607

Ok,then. Do it.

I must tell you how much your help means to me. I never said that and meant it at the same time. Now I do.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 89,048

The first application of RRA:

only 3000 terms necessary for 10 place accuracy.

**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: 15,607

I guess that we can get even more juice out of that lemon.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 89,048

After 12 iterations of the algorithm:

We have to sum:

Which is more than 11 digits of accuracy from only 21 terms!

**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: 15,607

Awesome! But why are there commas in the expression?

Can you now show me what the algorithm actually does i.e. What method it uses?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 89,048

Commas removed for plus signs. The latexing takes longer than the calculation!

**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: 15,607

Haha,that is true.

You told me you would show me the method now.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 89,048

Yes, can it wait till later because I am going to eat and it will take time to prepare a proper example and to latex it up?

**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: 15,607

Can you post it as soon as you can so that I can see it first thing in the morning?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 89,048

Yes, I will post it up after I cook and eat. I will need to explain it. So it will

carry on into tomorrow.

**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: 15,607

Ok. Don't overdo it. Yoy can post most of it and leave the rest for when you get up. See you tomorrow and again,congratultions!!!

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 89,048

Thanks! We will have some fun tomorrow with it. Hopefully we will look at 5 or 6

other acceleration techniques.

**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: 15,607

Of course we will! See you tomorrow!

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