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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,603

Hi

Can anyone help me with the following limit:

I know that it should be equal to 1/2 and the the Stolz theorem is supposed to be used, but I cannot get the final result...

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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: 88,788

**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: 15,603

No. I already looked at that page. It just gets the limit to the indeterminate from 0*infinity...

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: 88,788

We need to use the binomial theorem here now.

**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: 15,603

Do you see the n/(p+1) part? It makes it not possible to use Stolz like that.

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: 88,788

We are not allowed to split that limit?

Probably not, the two pieces are both equal to infinity.

**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: 15,603

That is right.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,788

I am trying to put it into the required form but the algebra is hideous.

The above limit equals 1 / 2 . But the limit is very difficult to handle.

**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
- Posts: 15,603

I already got that much. That limit there is the problem...

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,788

You got that far! How the heck did you get there?

Maybe we can use Stolz again?

**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
- Posts: 15,603

It wasn't hard.

I don't think ot would get much prettier...

*Last edited by anonimnystefy (2013-01-06 12:13:11)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,788

Why do you think this is a job for Stoltz then?

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**scientia****Member**- Registered: 2009-11-13
- Posts: 222

bobbym wrote:

The above limit equals 1 / 2 . But the limit is very difficult to handle.

Consider the numerator (ignoring the minus sign outside the fraction). Notice that the terms in and vanish so the highest power of is . Its coefficient is . Now look at the denominator. The highest power of is also and its coefficient is . Hence the limit as is

using the following rule:

If

and

and then*Last edited by scientia (2013-01-06 21:52:47)*

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,603

Wow! That is amazing! Thank you!

*Last edited by anonimnystefy (2013-01-06 13:17:45)*

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**scientia****Member**- Registered: 2009-11-13
- Posts: 222

You're welcome.

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