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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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you sneaky little...

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,737

**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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,673

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,737

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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,737

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

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**anonimnystefy****Real Member**- From: The Foundation
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hi bobbym

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**bobbym****Administrator**- From: Bumpkinland
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Not true.

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

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**anonimnystefy****Real Member**- From: The Foundation
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no?but wolfram said that they don't converge.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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What did you enter?

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**anonimnystefy****Real Member**- From: The Foundation
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is the ans 0?

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**bobbym****Administrator**- From: Bumpkinland
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Yes, and there is a very good argument for that.

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

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**anonimnystefy****Real Member**- From: The Foundation
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and that is?

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**bobbym****Administrator**- From: Bumpkinland
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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.**

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**anonimnystefy****Real Member**- From: The Foundation
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yes...

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**bobbym****Administrator**- From: Bumpkinland
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Have you heard of Stirling's formula or approximation?

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

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**anonimnystefy****Real Member**- From: The Foundation
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no,but i know that e^n is O(n^(n+1/2))

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**bobbym****Administrator**- From: Bumpkinland
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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.**

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**anonimnystefy****Real Member**- From: The Foundation
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ok

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**bobbym****Administrator**- From: Bumpkinland
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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.

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**anonimnystefy****Real Member**- From: The Foundation
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ok.

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**bobbym****Administrator**- From: Bumpkinland
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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.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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it does.so our limit is:

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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That is close:

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

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