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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,603

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,788

You had a denominator that was too large.

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**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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,788

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 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: 15,603

Hi bobbym

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

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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: 88,788

Hi;

I am not following you. What are you getting?

**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: 15,603

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

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: 88,788

Hi;

After 8 iterations of the algorithm I get:

That is quite close for only summing 19 terms!

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,603

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Point is, it is converging. Looking the bottom series of all positive terms. Do you not see convergence? How many iterations did you do?

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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I see the convergence, but I applied the RRA only 2 times.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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So you got 1 /10 + 1 / 45? Isn't that close to the answer?

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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It is. But the sum we get doesn't converge as fast as we'd like it to.

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**bobbym****Administrator**- From: Bumpkinland
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Whoa! Do you know many terms you would need of the original series to get the accuracy you have got

from just 2 iterations?

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,603

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?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,788

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?

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,603

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.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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You will first need to ascertain the accuracy of the answer we are getting without knowing the real answer!

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,603

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.

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**bobbym****Administrator**- From: Bumpkinland
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You are confusing the methods of numerical mathematics with the methods you have been taught. You are confusing the discrete with the continuous.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,603

Which part of my post are you referring to?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Has to be the second paragraph. The first is an error.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,603

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

And why is the first part an error?

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**bobbym****Administrator**- From: Bumpkinland
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The first sentence is clearly wrong.

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

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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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?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,788

How about showing me what you call a Leibniz series.

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