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## #76 2012-04-03 18:16:25

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

### Re: Find the general term!!!

Hi,

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

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

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## #77 2012-04-03 18:20:06

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,186

### Re: Find the general term!!!

Hi;

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #78 2012-04-03 19:19:53

bob bundy
Moderator
Registered: 2010-06-20
Posts: 7,743

### Re: Find the general term!!!

hi bobbym,

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

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #79 2012-04-03 19:29:42

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,186

### Re: Find the general term!!!

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #80 2012-04-03 22:25:33

bob bundy
Moderator
Registered: 2010-06-20
Posts: 7,743

### Re: Find the general term!!!

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

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #81 2012-04-03 23:31:18

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,186

### Re: Find the general term!!!

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #82 2012-04-04 00:23:27

bob bundy
Moderator
Registered: 2010-06-20
Posts: 7,743

### Re: Find the general term!!!

hi bobbym,

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

Thanks a lot.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #83 2012-04-04 00:30:53

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,186

### Re: Find the general term!!!

Hi bob bundy;

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #84 2012-04-04 06:02:07

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,018

### Re: Find the general term!!!

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
The knowledge of some things as a function of age is a delta function.

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## #85 2012-04-04 06:05:20

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,186

### Re: Find the general term!!!

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #86 2012-04-04 06:23:35

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,018

### Re: Find the general term!!!

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
The knowledge of some things as a function of age is a delta function.

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## #87 2012-04-04 06:25:14

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,186

### Re: Find the general term!!!

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #88 2012-04-04 06:30:52

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,018

### Re: Find the general term!!!

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
The knowledge of some things as a function of age is a delta function.

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## #89 2012-04-04 06:46:28

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,186

### Re: Find the general term!!!

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #90 2012-04-26 08:45:02

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,018

### Re: Find the general term!!!

#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.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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## #91 2012-04-26 08:51:36

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,186

### Re: Find the general term!!!

Hi;

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #92 2012-04-26 08:57:28

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,018

### Re: Find the general term!!!

That is correct!Can I see your generating function?

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
The knowledge of some things as a function of age is a delta function.

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## #93 2012-04-26 08:58:26

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,186

### Re: Find the general term!!!

No, you may not.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #94 2012-04-26 09:02:00

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,018

### Re: Find the general term!!!

Why not?Do you have one?

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
The knowledge of some things as a function of age is a delta function.

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## #95 2012-04-26 09:04:42

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,186

### Re: Find the general term!!!

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #96 2012-04-26 09:06:56

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,018

### Re: Find the general term!!!

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
The knowledge of some things as a function of age is a delta function.

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## #97 2012-04-26 09:09:27

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,186

### Re: Find the general term!!!

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #98 2012-04-26 09:12:35

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,018

### Re: Find the general term!!!

Why not?

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
The knowledge of some things as a function of age is a delta function.

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## #99 2012-04-26 09:14:03

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,186

### Re: Find the general term!!!

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #100 2012-04-26 09:17:57

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,018

### Re: Find the general term!!!

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.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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