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#176 2011-09-15 09:17:22

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Series

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.
Always satisfy the Prime Directive of getting the right answer above all else.

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#177 2011-09-15 09:22:07

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

Re: Series

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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#178 2011-09-15 09:27:06

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Series

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.
Always satisfy the Prime Directive of getting the right answer above all else.

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#179 2011-09-16 00:06:30

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Series

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.
Always satisfy the Prime Directive of getting the right answer above all else.

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#180 2011-09-16 04:42:35

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

Re: Series

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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#181 2011-09-16 06:26:00

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Series

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.
Always satisfy the Prime Directive of getting the right answer above all else.

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#182 2011-09-16 18:33:02

gAr
Member
Registered: 2011-01-09
Posts: 3,481

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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#183 2011-09-16 21:29:53

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

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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#184 2011-09-16 22:08:51

gAr
Member
Registered: 2011-01-09
Posts: 3,481

Re: Series

"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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#185 2011-09-17 02:22:04

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Series

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.
Always satisfy the Prime Directive of getting the right answer above all else.

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#186 2011-09-17 15:11:38

gAr
Member
Registered: 2011-01-09
Posts: 3,481

Re: Series

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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#187 2011-09-18 03:11:11

Member
Registered: 2011-05-11
Posts: 171

Re: Series

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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I wish a had a more interesting signature line.

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#188 2011-09-18 21:03:05

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Series

Hi;

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.
Always satisfy the Prime Directive of getting the right answer above all else.

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#189 2011-09-19 02:14:07

Member
Registered: 2011-05-11
Posts: 171

Re: Series

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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#190 2011-09-19 02:17:21

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Series

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.
Always satisfy the Prime Directive of getting the right answer above all else.

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#191 2011-09-19 02:48:27

Member
Registered: 2011-05-11
Posts: 171

Re: Series

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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#192 2011-09-22 17:30:33

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Series

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.
Always satisfy the Prime Directive of getting the right answer above all else.

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#193 2011-09-26 01:06:01

gAr
Member
Registered: 2011-01-09
Posts: 3,481

Re: Series

22)

Show that

"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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#194 2012-02-17 05:52:56

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

Re: Series

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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#195 2012-02-17 05:58:58

gAr
Member
Registered: 2011-01-09
Posts: 3,481

Re: Series

Nope, only after all the sums here are solved!

"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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#196 2012-02-17 06:01:55

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

Re: Series

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

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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#197 2012-02-20 05:33:26

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

Re: Series

hi gAr

just wanna ask if this is ok:

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

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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#198 2012-02-20 10:30:53

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Series

Hi 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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#199 2012-02-21 02:19:06

gAr
Member
Registered: 2011-01-09
Posts: 3,481

Re: Series

Hi anonimnystefy,

I did the problem bobbym's way.

"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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#200 2012-02-21 03:52:07

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

Re: Series

hi guys

i looked for formulas for

but the only one i found was the one i 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.

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