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## #51 2012-04-12 01:18:29

anonimnystefy
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### Re: The RRA

Why didn't it output right to me,then?

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

## #52 2012-04-12 01:30:10

bobbym

Online

### Re: The RRA

You had a denominator that was too large.

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.

## #53 2012-04-12 08:55:56

bobbym

Online

### Re: The RRA

Estimate the following sum for a PSLQ to 16 digits of precision. I would like to only sum 20 or so terms. Develope a new series that converges that fast.

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.

## #54 2012-07-12 14:23:17

anonimnystefy
Real Member

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### Re: The RRA

Hi bobbym

The number of terms needed doesn't seem to be going down.

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

## #55 2012-07-12 20:07:26

bobbym

Online

### Re: The RRA

Hi;

I am not following you. What are you getting?

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.

## #56 2012-07-13 00:20:24

anonimnystefy
Real Member

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### Re: The RRA

When I apply the RRA it doesn't shrink down the number of terms needed.

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

## #57 2012-07-13 00:29:48

bobbym

Online

### Re: The RRA

Hi;

After 8 iterations of the algorithm I get:

That is quite close for only summing 19 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.

## #58 2012-07-13 00:35:08

anonimnystefy
Real Member

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### Re: The RRA

Eight iterations! I do not have that capability by hand and I don't yet have a program to do it for me.

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

## #59 2012-07-13 03:30:15

bobbym

Online

### Re: The RRA

Point is, it is converging. Looking the bottom series of all positive terms. Do you not see convergence? How many iterations did you do?

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.

## #60 2012-07-13 04:00:22

anonimnystefy
Real Member

Offline

### Re: The RRA

I see the convergence, but I applied the RRA only 2 times.

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

## #61 2012-07-13 04:05:16

bobbym

Online

### Re: The RRA

So you got 1 /10 + 1 / 45? Isn't that close to the answer?

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.

## #62 2012-07-13 04:09:35

anonimnystefy
Real Member

Offline

### Re: The RRA

It is. But the sum we get doesn't converge as fast as we'd like it to.

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

## #63 2012-07-13 04:14:44

bobbym

Online

### Re: The RRA

Whoa! Do you know many terms you would need of the original series to get the accuracy you have got
from just 2 iterations?

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.

## #64 2012-07-21 10:56:55

Imdat
Guest

### Re: The RRA

That's a pretty good idea and i will look into that.  But that's a very broad topic.  In the mean time if you join one of the forum grpuos like  open discussion   you can post any questions you may have about claimers and i am sure someone will help you out.

## #65 2012-07-21 11:26:52

anonimnystefy
Real Member

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### Re: The RRA

#### bobbym wrote:

Whoa! Do you know many terms you would need of the original series to get the accuracy you have got
from just 2 iterations?

No. How many?

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

## #66 2012-07-21 12:59:50

bobbym

Online

### Re: The RRA

You have forgotten how to get it? Or you never learned it from our discussions of Taylor series?
Or you are not the same guy?

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.

## #67 2012-07-21 13:26:08

anonimnystefy
Real Member

Offline

### Re: The RRA

I am the same guy, but I do not like typing math expressions into Wolfram while on the phone. I will do it as soon as I get to my laptop.

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

## #68 2012-07-21 13:28:07

bobbym

Online

### Re: The RRA

You will first need to ascertain the accuracy of the answer we are getting without knowing the real answer!

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.

## #69 2012-07-21 13:34:57

anonimnystefy
Real Member

Offline

### Re: The RRA

Why do that? I just set the tail equal to the desired accuracy and solve it in WA. That is the least I could remember.

While I was in the mountains, I managed once to get a wireless connection and see the latest baffler. When I realized what the first differences are I needed to get the first 50 or so digits of pi. I wanted to use the Leibniz formula, but I remembered that it converges slowly so I applied RRA. I got another series that is the result of applying the RRA infinitely many times which involved a double factorial, but the new series wasn't particularly fast either. My confidence in the RRA was then shaken. But at least I tried to use it.

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

## #70 2012-07-21 13:36:45

bobbym

Online

### Re: The RRA

You are confusing the methods of numerical mathematics with the methods you  have been taught. You are confusing the discrete with the continuous.

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.

## #71 2012-07-21 13:43:02

anonimnystefy
Real Member

Offline

### Re: The RRA

Which part of my post are you referring to?

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

## #72 2012-07-21 13:44:03

bobbym

Online

### Re: The RRA

Has to be the second paragraph. The first is an error.

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.

## #73 2012-07-21 13:47:49

anonimnystefy
Real Member

Offline

### Re: The RRA

What is the part I have done wrong while calculating pi?

And why is the first part an error?

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

## #74 2012-07-21 13:50:02

bobbym

Online

### Re: The RRA

The first sentence is clearly wrong.

The second paragraph violates the properties that are inherent in the way numerical math is done.

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.

## #75 2012-07-21 13:54:01

anonimnystefy
Real Member

Offline

### Re: The RRA

Yeah, not the whole tail. I set the absolute value of the general term to the 0.5*10**number of accurate digits required and solve it to get how many terms I need to sum.

What properties?

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