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Topic: Sequence limit
Replies: 72   Last Post: Nov 26, 2013 12:07 AM

 Messages: [ Previous | Next ]
 karl Posts: 397 Registered: 8/11/06
Re: Sequence limit
Posted: Oct 27, 2013 9:31 AM

Am 26.10.2013 10:41, schrieb christian.bau:
> On Saturday, October 26, 2013 8:13:31 AM UTC+1, Roland Franzius wrote:
>
> Excellent and highly relevant post.
>
> So the situation is this:
>
> For real numbers anyone but the most inexperienced see immediately that the limit
>
> lim |sin (x)|^(1/x)
> x>inf
>
> doesn't exist, because there are arbitrarily large values x where |sin (x)|^(1/x) is 0, and arbitrarily large values x where |sin (x)|^(1/x) is 1,
>
> If x is restricted to integers, then it is obvious that
>
> lim f (x)^(1/x)
> x->inf
>
> is 1 if f (x) has a lower bound greater than 1 and an upper bound. Only slightly less obvious is that if f (x) has an upper bound and f (x) > 0 for all x (which it is in our case) and we take the subsequence of x's which make f (x) closer to 0 than for any smaller x, and lim f (x)^(1/x) is 1 for that subsequence, then it is 1 for the whole sequence.
>
> Roland's post demonstrated that it is most likely that the limit is 1.
>

Ok, you know the joke, how engineers prove that all odd number are prime?
Where is the difference?

Date Subject Author
10/3/13 Bart Goddard
10/3/13 Karl-Olav Nyberg
10/3/13 quasi
10/3/13 quasi
10/3/13 Karl-Olav Nyberg
10/3/13 quasi
10/4/13 Roland Franzius
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10/5/13 Roland Franzius
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10/26/13 Roland Franzius
10/26/13 karl
10/26/13 Roland Franzius
10/26/13 gnasher729
10/27/13 karl
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10/4/13 Leon Aigret
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10/4/13 David C. Ullrich
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10/6/13 David Bernier
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10/7/13 fom
10/8/13 Virgil
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10/4/13 fom
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10/9/13 Shmuel (Seymour J.) Metz
10/10/13 Bart Goddard
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11/11/13 Shmuel (Seymour J.) Metz
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11/15/13 Shmuel (Seymour J.) Metz
11/15/13 Bart Goddard
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11/8/13 Bart Goddard
11/8/13 Paul
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