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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,249

You might try using the Binet formula hoping that there would be some cancellation. Or you can try expanding the first few terms and trying to recognize the generating function.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,016

i don't know any of that stuff.what about 19?

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,249

19, possibly snake oil method. Or again using a table to recognize the generating function.

Also you really should know the Binet formula.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,249

Hi gAr;

Hopefully, you have a subscribe and solutions on this thread might draw you back.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,016

where can i find it?

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,249

It? The fountain of youth? The Oracle at Delphi? The room beneath the Sphinx? The ark of the Covenant? King Solomons gold? Brad Pitts ambition? Darth Vader's and the Cowardly Lion's courage? The opening to the alien base beneath Vegas?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,249

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.****No great discovery was ever made without a bold guess. **

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

"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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,249

Hi gAr;

The best of luck to you.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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

Hi bobbym,

Thank you!

"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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**reconsideryouranswer****Member**- Registered: 2011-05-11
- Posts: 171

Is this convergent or divergent?

Please look at this amended pronblem. (All variables are the same now.)

*Last edited by reconsideryouranswer (2011-09-19 02:47:14)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,249

Hi;

reconsideryouranswer wrote:

Since;

Has no solutions, the summand is a constant and an infinite sum of constants does not converge.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**reconsideryouranswer****Member**- Registered: 2011-05-11
- Posts: 171

bobbym wrote:

Hi;

Since;

1)

2) Has no solutions,

the summand is a constant

and an infinite sum of constants does not converge.

1)

You meant the *limit of that expression as x --> oo*, correct?

Can you justify this?

2)

So, I don't see your first part of your message as being sufficient

to justify that the sum is divergent (not convergent).

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I wish a had a more interesting signature line.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,249

Your 2) is incorrect. That only applies when the x is part of the indices:

Which is not the same as:

The top one is adding up a sequence that is getting smaller and it converges. The second one is adding up a sequence that never changes, it diverges.

You do not need limits here. There is no value that can make the summand = 0. Therefore for all values of x the summand is a constant. It never changes, Add up an infinite bunch of constants and you have a divergent series.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**reconsideryouranswer****Member**- Registered: 2011-05-11
- Posts: 171

reconsideryouranswer wrote:

Is this convergent or divergent?

Please look at this amended problem. (All variables are the same now.)

-----------------------------------------------------------------------

-----------------------------------------------------------------------

bobbym wrote:

"Since;

Has no solutions, ..."

There was a misunderstanding here by me,

because you didn't put this all on one line**,

and you had "Has" in the middle of a

sentence instead of "has." It appears to

be two sentences, despite "Since;[,]"

being at the beginning of the sentence.

** It is just about the visual aspect of it not being on

one line, not the correctness of it.

*** Edit:

My amended question is still open.

*Last edited by reconsideryouranswer (2011-09-19 03:07:11)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,249

Hi reconsideryouranswer;

First observe:

Using the comparison test:

The RHS is a variant of the harmonic series and is known to diverge. In order for that inequality to be true then:

must be true.

Raise both sides to the n^n th power:

This is obvious for all n>=1. This now implies:

Since your sum is greater than a known series that diverges by the comparison test it too diverges.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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

**22)**

Show that

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

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,016

any easier sums?

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

Nope, only after all the sums here are solved!

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

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,016

but i don't know how to solve these sums.that's why i asked for some easier ones.

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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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,016

hi gAr

just wanna ask if this is ok:

*Last edited by anonimnystefy (2012-02-20 05:39:18)*

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,249

Hi anonimnystefy;

Your #17 is not correct.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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

Hi anonimnystefy,

I did the problem bobbym's way.

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

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,016

hi guys

i looked for formulas for

but the only one i found was the one i used.

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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