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## #626 2012-04-11 09:41:15

anonimnystefy
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### Re: Oh,Oh,Oh,merry analysis!!!

44721 terms?

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
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #627 2012-04-11 09:46:59

bobbym

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### Re: Oh,Oh,Oh,merry analysis!!!

I do not think that is enough.

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #628 2012-04-11 09:52:30

anonimnystefy
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### Re: Oh,Oh,Oh,merry analysis!!!

Are you 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
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #629 2012-04-11 09:59:54

bobbym

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### Re: Oh,Oh,Oh,merry analysis!!!

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 have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #630 2012-04-11 10:09:09

anonimnystefy
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### Re: Oh,Oh,Oh,merry analysis!!!

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...

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
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #631 2012-04-11 10:11:03

bobbym

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### Re: Oh,Oh,Oh,merry analysis!!!

Hi;

When I solve it I got n = 141421.356

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #632 2012-04-11 10:12:22

anonimnystefy
Real Member

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### Re: Oh,Oh,Oh,merry analysis!!!

Could you show me your steps?

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
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #633 2012-04-11 10:17:30

bobbym

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### Re: Oh,Oh,Oh,merry analysis!!!

Times both sides by n^2.

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #634 2012-04-11 10:22:03

anonimnystefy
Real Member

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### Re: Oh,Oh,Oh,merry analysis!!!

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

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
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #635 2012-04-11 10:24:18

bobbym

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### Re: Oh,Oh,Oh,merry analysis!!!

There are many ways but we are doing the RRA.

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #636 2012-04-11 10:28:49

anonimnystefy
Real Member

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### Re: Oh,Oh,Oh,merry analysis!!!

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

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
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #637 2012-04-11 10:39:06

bobbym

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### Re: Oh,Oh,Oh,merry analysis!!!

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #638 2012-04-11 10:41:36

anonimnystefy
Real Member

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### Re: Oh,Oh,Oh,merry analysis!!!

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.

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
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #639 2012-04-11 10:46:30

bobbym

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### Re: Oh,Oh,Oh,merry analysis!!!

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #640 2012-04-11 10:48:14

anonimnystefy
Real Member

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### Re: Oh,Oh,Oh,merry analysis!!!

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

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
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #641 2012-04-11 11:03:23

bobbym

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### Re: Oh,Oh,Oh,merry analysis!!!

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #642 2012-04-11 11:06:32

anonimnystefy
Real Member

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### Re: Oh,Oh,Oh,merry analysis!!!

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?

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
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #643 2012-04-11 11:07:59

bobbym

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### Re: Oh,Oh,Oh,merry analysis!!!

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #644 2012-04-11 11:09:29

anonimnystefy
Real Member

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### Re: Oh,Oh,Oh,merry analysis!!!

Haha,that is true.

You told me you would show me the method now.

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
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #645 2012-04-11 11:10:35

bobbym

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### Re: Oh,Oh,Oh,merry analysis!!!

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #646 2012-04-11 11:14:08

anonimnystefy
Real Member

Offline

### Re: Oh,Oh,Oh,merry analysis!!!

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

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
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #647 2012-04-11 11:16:03

bobbym

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### Re: Oh,Oh,Oh,merry analysis!!!

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #648 2012-04-11 11:18:25

anonimnystefy
Real Member

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### Re: Oh,Oh,Oh,merry analysis!!!

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!!!

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
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #649 2012-04-11 11:25:19

bobbym

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### Re: Oh,Oh,Oh,merry analysis!!!

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #650 2012-04-11 11:27:17

anonimnystefy
Real Member

Offline

### Re: Oh,Oh,Oh,merry analysis!!!

Of course we will! See you tomorrow!

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
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment