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#451 2012-02-19 14:33:36

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

Re: Limits!

Hi bobbym,

What is the limit of a_n as n approaches infinity, with a being any real number.


"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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#452 2012-02-19 14:37:22

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,481

Re: Limits!

Very good! You found the link, I was hiding it!


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#453 2012-02-19 14:49:00

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

Re: Limits!

Thanks!
Do you want me to erase the link?


"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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#454 2012-02-19 16:16:15

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,481

Re: Limits!

No, that is okay. I was just teasing him.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#455 2012-02-19 16:33:29

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

Re: Limits!

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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#456 2012-02-19 20:52:58

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,481

Re: Limits!

Hi gAr;

Did you know to do that one before you found the link?


Hi anonimnystefy;

See post #450.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#457 2012-02-19 21:25:30

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

Re: Limits!

Hi bobbym,

I tried for sometime, but didn't get the solution. Then I searched for the link.


"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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#458 2012-02-19 21:51:47

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,481

Re: Limits!

Hi;

I was unable to get it either.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#459 2012-02-19 22:33:43

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

Re: Limits!

Summations with flooring and ceiling are a bit difficult for me.


"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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#460 2012-02-20 00:16:00

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,481

Re: Limits!

I agree, it is very hard to eliminate them.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#461 2012-02-20 02:48:19

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: Limits!

hi bobbym


“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

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#462 2012-02-20 05:17:21

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,481

Re: Limits!

Hi;

No problem is too easy!


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#463 2012-02-20 05:43:08

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: Limits!

hi bobbym


“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

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#464 2012-02-20 05:46:28

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,481

Re: Limits!

Very good!


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#465 2012-02-20 05:49:02

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: Limits!

hi bobbym

next one?

and if you can,please check my attempt at the series #17 problem.tell me if it's good at all.if not i want to change my direction so that i don't waste my time on wrong attempts. smile


“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

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#466 2012-02-20 05:55:41

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,481

Re: Limits!


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#467 2012-02-20 06:04:44

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: Limits!

hi bobbym

my new friend Maxima says it's


“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

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#468 2012-02-20 06:12:33

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,481

Re: Limits!

What do you say it is?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#469 2012-02-20 06:13:59

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: Limits!

hi bobbym


“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

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#470 2012-02-20 06:15:43

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,481

Re: Limits!

How do you go about getting such an answer?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#471 2012-02-20 06:33:29

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: Limits!

hi bobbym

i'm not sure.maybe because e/x tends to zero when x goes to infinity,and 0^'infinity' tends to zero? i'm just guessing because i tried to do the l'Hopital's rule,but i got some pretty nasty functions.


“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

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#472 2012-02-20 06:35:52

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,481

Re: Limits!

Do you at least have some empirical evidence?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#473 2012-02-20 06:43:50

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: Limits!

hi bobbym

wolfram won't work it out for x=100 or x=1000. think there's no sense in going larger.


“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

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#474 2012-02-20 06:50:03

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,481

Re: Limits!

Did you know that Maxima can do arithmetic that dwarfs Mathematica's puny efforts.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#475 2012-02-26 04:20:54

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: Limits!

Hi bobbym

I haven't done this on Maxima yet, but I'm sure that the answer is 0.

maybe another way could be using a substitution y=e^x.


“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

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