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#326 2012-02-16 09:36:13

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 88,882

Re: Limits!

Correct! Wanted to see if you were sure.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#327 2012-02-16 09:36:49

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,606

Re: Limits!

tongue you sneaky little... big_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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#328 2012-02-16 09:43:53

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,882

Re: Limits!


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#329 2012-02-16 10:00:18

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,606

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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#330 2012-02-16 10:03:22

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,882

Re: Limits!

Correct!


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#331 2012-02-16 10:06:09

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,606

Re: Limits!

hi bobbym

why are you giving these easy 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

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#332 2012-02-16 10:10:59

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,882

Re: Limits!


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#333 2012-02-16 10:17:09

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,606

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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#334 2012-02-16 10:17:48

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 88,882

Re: Limits!

Not true.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#335 2012-02-16 10:35:24

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,606

Re: Limits!

no?but wolfram said that they don't converge.


“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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#336 2012-02-16 10:36:49

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,882

Re: Limits!

What did you enter?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#337 2012-02-16 10:45:12

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,606

Re: Limits!

is the ans 0?


“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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#338 2012-02-16 10:46:54

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,882

Re: Limits!

Yes, and there is a very good argument for that.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#339 2012-02-16 10:50:49

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,606

Re: Limits!

and that is?


“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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#340 2012-02-16 10:57:27

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,882

Re: Limits!

Do you agree that we can write the above limit in this more convenient form:


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#341 2012-02-16 11:03:51

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,606

Re: Limits!

yes...


“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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#342 2012-02-16 11:07:53

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,882

Re: Limits!

Have you heard of Stirling's formula or approximation?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#343 2012-02-16 11:14:42

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,606

Re: Limits!

no,but i know that e^n is O(n^(n+1/2)) big_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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#344 2012-02-16 11:19:16

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,882

Re: Limits!

Okay, Stirling's formula was discovered by James Stirling and is a very good approximation for factorials. It is used quite often in many fields of mathematiocs.

1)First convince yourself that

f(100) is a good approximation of 100!


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#345 2012-02-16 11:33:21

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,606

Re: Limits!

ok


“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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#346 2012-02-16 11:41:34

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,882

Re: Limits!

Now it is important to understand that

but more importantly

This means that Stirling's formula becomes a better and better approximation of n! the larger n gets.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#347 2012-02-16 11:43:57

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,606

Re: Limits!

ok.


“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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#348 2012-02-16 11:46:45

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,882

Re: Limits!

Remember the result in #340?

and Stirlings formula?

Does not the RHS of 1) look like the LHS of 2 inverted?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#349 2012-02-16 11:49:24

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,606

Re: Limits!

it does.so our limit is:

Last edited by anonimnystefy (2012-02-16 11:49:51)


“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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#350 2012-02-16 11:52:32

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,882

Re: Limits!

That is close:


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

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