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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi,

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,879

Hi;

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

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,538

hi bobbym,

Glad you've picked up on this thread.

If you get time have a look at posts 30 to 45. Did we get this sorted?

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,879

Hi Bob;

I see lots of gAr and you in here and that means I can do something else.

My friend poses 100 problems a second and rarely stops to look around. gAr is correct about the continued radical solving #2.

Which one got away from gAr and you?

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

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,538

hi Bobbym

post 30

with

Stefy wanted the general term.

gAr and I could give him the convergence, but don't think there will be a simple formula.

What do you think?

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,879

Hi Bob;

There is nothing simple that I can find.

Except an error analysis produces this which is an asymptotic answer

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

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,538

hi bobbym,

Well that's quite a good result. I'm happy with that.

Thanks a lot.

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,879

Hi bob bundy;

Your welcome.

**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: 15,673

bobbym wrote:

Hi;

Why is it impossible?

gAr wrote:

Hi,

What is you GF?

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: 90,879

That is kind of easy to reason about. You need to think about that yourself. If you do not get it then you need some work in algebra, which is even more fundamental than calculus.

Post #81 shows the power of the new experimental mathematics.

**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: 15,673

Yes I saw #81.Nice work on that.

I will se why #5 is impossible.

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: 90,879

Did you try it out before complimenting me? Could be wrong... How would you convince yourself that it might do what it claims?

**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: 15,673

Hi bobbym

I checked the first few terms.How did you arrive at that formula? *please don't say CAS,please don't say Cas,...*

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: 90,879

Hi;

It is derived easily with some guessing and what I think I know about error analysis. This is not a mathematicians way of working. I told you and have shown you the tools necessary to do this kind of work. I have not yet convinced you over to my way but I have noticed that you are envious of the type of answers gAr is capable of.

When you are convinced we will go further. For now let's look at the empirical evidence.

Supposing you wanted to know as close as possible what the 200th term in your recurrence was.

Using the formula we get

The exact answer to 100 digits is:

Pretty good!

**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: 15,673

**#6)Find the generating function of the sequence:**

**and from the generating function deduce the general term.**

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,879

Hi;

**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: 15,673

That is correct!Can I see your generating function?

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,879

No, you may 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: 15,673

Why not?Do you have one?

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,879

It is possible to derive the GF. But that is not necessary here. There is a much better and shorter way.

**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: 15,673

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,879

That method will not get what you require, because it is not the correct method to solve the problem.

**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: 15,673

Why not?

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,879

You are getting ahead of yourself. Confusing yourself further, the answer lies in the other thread!

**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: 15,673

Which other thread? There are so many of them!

You could get the generating function by forming a recurrence formula for the series and then finding the GF from there.

Here lies the reader who will never open this book. He is forever dead.

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