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## #1 2014-05-20 23:52:05

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 23,170
Website

### Prove Divergence

Does this diverge?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #2 2014-05-21 16:32:30

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 102,229

### Re: Prove Divergence

Hi;

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
A number by itself is useful, but it is far more useful to know how accurate or certain that number is.

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## #3 2014-05-21 16:33:11

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,000

### Re: Prove Divergence

Heh, it' like Veronica Roth's book.

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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## #4 2014-05-21 16:39:02

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 102,229

### Re: Prove Divergence

Veronica who?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
A number by itself is useful, but it is far more useful to know how accurate or certain that number is.

Online

## #5 2014-05-21 17:23:25

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,000

### Re: Prove Divergence

Roth. She's a writer.

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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## #6 2014-05-21 17:30:57

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 23,170
Website

### Re: Prove Divergence

I'm getting divergent only because M cannot get the sum.

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #7 2014-05-21 19:33:20

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 102,229

### Re: Prove Divergence

Do the integration.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
A number by itself is useful, but it is far more useful to know how accurate or certain that number is.

Online

## #8 2014-05-21 19:38:09

zetafunc
Member
Registered: 2014-05-21
Posts: 1,090
Website

### Re: Prove Divergence

The function can be shown to not be integrable, which would show that it diverges via the integral test -- but on the other hand, you would have to show that f is monotone decreasing on [1,infinity) before you can use that test, and I'm not sure if it is...

Last edited by zetafunc (2014-05-25 03:08:56)

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## #9 2014-05-21 19:40:13

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 102,229

### Re: Prove Divergence

Yes, it is not but after a certain point it might be...

Anyway, that was not the test I used.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
A number by itself is useful, but it is far more useful to know how accurate or certain that number is.

Online

## #10 2014-05-21 20:20:01

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,000

### Re: Prove Divergence

It is not monotone.

Which test have you used?

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.

Offline

## #11 2014-05-21 20:22:22

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 23,170
Website

### Re: Prove Divergence

How am I supposed to do the integration?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #12 2014-05-21 20:23:39

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 102,229

### Re: Prove Divergence

I suggested it to Agnishom because I was hoping he would integrate and then ask about whether he could use the fact that if the integral exists then the sum exists...

That one takes some doing numerically to convince that it diverges and then I just looked up the rest.

I will post the main link if you want it.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
A number by itself is useful, but it is far more useful to know how accurate or certain that number is.

Online

## #13 2014-05-21 20:38:55

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 23,170
Website

### Re: Prove Divergence

I have no clue on how to show if no integral exists

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #14 2014-05-21 21:07:28

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 102,229

### Re: Prove Divergence

The test does not apply? But you do not know how to integrate that even with M?

There is even a nice video on it.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
A number by itself is useful, but it is far more useful to know how accurate or certain that number is.

Online