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#1 2013-01-07 08:45:52

anonimnystefy
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A weird limit!

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...


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#2 2013-01-07 09:12:31

bobbym
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Re: A weird limit!


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#3 2013-01-07 09:25:07

anonimnystefy
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Re: A weird limit!

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


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#4 2013-01-07 09:51:59

bobbym
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Re: A weird limit!









We need to use the binomial theorem here now.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#5 2013-01-07 09:54:32

anonimnystefy
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Re: A weird limit!

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


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#6 2013-01-07 09:57:02

bobbym
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Re: A weird limit!

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 have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#7 2013-01-07 10:07:31

anonimnystefy
Real Member

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Re: A weird limit!

That is right.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#8 2013-01-07 10:14:58

bobbym
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Re: A weird limit!

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#9 2013-01-07 10:58:08

anonimnystefy
Real Member

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Re: A weird limit!

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


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#10 2013-01-07 11:04:05

bobbym
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Re: A weird limit!

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#11 2013-01-07 11:12:44

anonimnystefy
Real Member

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Re: A weird limit!

It wasn't hard.

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

Last edited by anonimnystefy (2013-01-07 11:13:11)


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#12 2013-01-07 11:42:20

bobbym
Administrator

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Re: A weird limit!

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


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#13 2013-01-07 11:51:08

scientia
Full Member

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Re: A weird limit!

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 (2013-01-07 20:52:47)

#14 2013-01-07 12:17:22

anonimnystefy
Real Member

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Re: A weird limit!

Wow! That is amazing! Thank you! smile

Last edited by anonimnystefy (2013-01-07 12:17:45)


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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