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## #126 2011-08-10 20:56:55

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

### Re: Series

Hi bobbym,

Yes, it's from that page.

"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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## #127 2011-08-10 21:02:04

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,648

### Re: Series

Hi gAr;

Cool, I will copy it.

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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## #128 2011-08-10 21:05:23

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

### Re: Series

I already have, with a dark ink!

I'm searching for more g.f's to experiment with.

"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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## #129 2011-08-10 21:06:28

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,648

### Re: Series

Hi;

I finished one but it wiil take time to write it up.

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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## #130 2011-08-10 21:11:10

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

### Re: Series

Hi bobbym,

Okay.

"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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## #131 2011-08-14 04:42:13

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

### Re: Series

14)

First question submitted by Ramanujan to the journal of the indian mathematical society

"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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## #132 2011-08-14 05:43:32

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

### Re: Series

hi gAr

is that log a natural logarithm or the common logarithm?

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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## #133 2011-08-14 05:58:11

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

### Re: Series

Hi,

It's a natural logarithm

"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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## #134 2011-08-16 01:54:05

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

### Re: Series

15)

Last edited by gAr (2011-08-16 01:55:33)

"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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## #135 2011-08-16 02:05:01

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,648

### Re: Series

Hiyo Silver!

I am zeroing in on that Ramanujan sum!

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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## #136 2011-08-16 02:10:54

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

### Re: Series

That's good!

"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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## #137 2011-08-16 09:05:14

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,648

### Re: Series

Hi gAr;

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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## #138 2011-08-16 11:39:26

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

### Re: Series

gAr wrote:

14)

i think i saw calculus.

yes i did see calculus.

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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## #139 2011-08-16 15:27:46

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,648

### Re: Series

Hi gAr;

anonimnystefy might be right. That might be calculus. I am not sure? Is integration calculus? I really do not know. Okay, it is calculus. But it is interesting anyway. I will keep looking for something else.

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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## #140 2011-08-16 15:30:07

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

### Re: Series

Hi bobbym,

"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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## #141 2011-08-16 15:41:10

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,648

### Re: Series

Hi gAr;

Yes, I know I was just kidding anonimnystefy.

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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## #142 2011-08-16 15:47:16

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

### Re: Series

Hi bobbym,

Okay!

"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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## #143 2011-08-16 15:50:12

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,648

### Re: Series

Hi gAr;

That is okay. I was working on the bounding of the sum. Thought it was a long shot. When I found that identity I forgot the conditions of the question.

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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## #144 2011-08-16 16:00:56

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

### Re: Series

Hi,

Okay.
Manipulating the sum was tricky from the solution I saw.
So I expanded it to a few terms to see what it actually looked like. Then I could understand.
Of course, the first step is partial fractions!

"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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## #145 2011-08-17 01:39:45

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

### Re: Series

16)

"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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## #146 2011-08-17 05:36:23

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,648

### Re: Series

Hi gAr;

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.

Offline

## #147 2011-08-17 05:50:56

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

### Re: Series

Hi bobbym,

"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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## #148 2011-08-17 05:53:41

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,648

### Re: Series

Hi gAr;

I am not following you. The series is to infinity and  the terms perfectly interleave so it is exactly the log(2) series. What did you do here?

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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## #149 2011-08-17 06:05:46

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

### Re: Series

Hi,

Roughly, I meant to say they travel unequal "distances" , that term 1/2k is a slowpoke!

"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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## #150 2011-08-17 06:08:59

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,648

### Re: Series

So how do you combine them up?

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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