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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,231

Re: Limits!

Correct! Wanted to see if you were sure.


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

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,544

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: 87,231

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

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

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: 87,231

Re: Limits!

Correct!


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

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

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: 87,231

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

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

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
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,231

Re: Limits!

Not true.


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

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

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: 87,231

Re: Limits!

What did you enter?


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

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

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: 87,231

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

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: 87,231

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

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: 87,231

Re: Limits!

Have you heard of Stirling's formula or approximation?


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

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

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: 87,231

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

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: 87,231

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

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: 87,231

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

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: 87,231

Re: Limits!

That is close:


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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