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

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quasi

Posts: 10,317
Registered: 7/15/05
Re: Sequence limit
Posted: Oct 4, 2013 4:26 AM
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William Elliot wrote:
>Bart Goddard wrote:
>

>> What is lim_{n -> oo} |sin n|^(1/n)
>>
>> where n runs through the positive integers.

>
>If lim(j->oo) a_(j+1)/aj = a, then lim(j->oo) aj^(1/j) = a.
>
>What's lim(j->oo) |(sin j+1)/sin j| ?
>
>|sin j cos 1 + cos j sin 1|/|sin j| = |cos 1 + cot j sin 1|,
> oh my.


If by a_n you mean |sin(n)| then what you've shown above is
that lim(n->oo)(a_(n+1)/a_n) does not exist.

But the nonexistence of that limit yields no information about
the existence or nonexistance of lim(n->oo)((a_n)^(1/n)).

quasi


Date Subject Author
10/3/13
Read Sequence limit
Bart Goddard
10/3/13
Read Re: Sequence limit
Karl-Olav Nyberg
10/3/13
Read Re: Sequence limit
quasi
10/3/13
Read Re: Sequence limit
quasi
10/3/13
Read Re: Sequence limit
Karl-Olav Nyberg
10/3/13
Read Re: Sequence limit
quasi
10/4/13
Read Re: Sequence limit
Roland Franzius
10/4/13
Read Re: Sequence limit
quasi
10/5/13
Read Re: Sequence limit
Roland Franzius
10/5/13
Read Re: Sequence limit
quasi
10/26/13
Read Re: Sequence limit
Roland Franzius
10/26/13
Read Re: Sequence limit
karl
10/26/13
Read Re: Sequence limit
Roland Franzius
10/26/13
Read Re: Sequence limit
gnasher729
10/27/13
Read Re: Sequence limit
karl
10/3/13
Read Re: Sequence limit
quasi
10/4/13
Read Re: Sequence limit
Leon Aigret
10/4/13
Read Re: Sequence limit
William Elliot
10/4/13
Read Re: Sequence limit
quasi
10/4/13
Read Re: Sequence limit
William Elliot
10/4/13
Read Re: Sequence limit
quasi
10/4/13
Read Re: Sequence limit
David C. Ullrich
10/4/13
Read Re: Sequence limit
Robin Chapman
10/5/13
Read Re: Sequence limit
Bart Goddard
10/4/13
Read Re: Sequence limit
GoogleOnly@mpClasses.com
10/4/13
Read Re: Sequence limit
Bart Goddard
10/4/13
Read Re: Sequence limit
GoogleOnly@mpClasses.com
10/4/13
Read Re: Sequence limit
Peter Percival
10/5/13
Read Re: Sequence limit
Virgil
10/4/13
Read Re: Sequence limit
Bart Goddard
10/6/13
Read Re: Sequence limit
David Bernier
10/6/13
Read Re: Sequence limit
Virgil
10/6/13
Read Re: Sequence limit
Bart Goddard
10/7/13
Read Re: Sequence limit
Mohan Pawar
10/7/13
Read Re: Sequence limit
Bart Goddard
10/7/13
Read Re: Sequence limit
gnasher729
10/7/13
Read Re: Sequence limit
Richard Tobin
10/7/13
Read Re: Sequence limit
Robin Chapman
10/7/13
Read Re: Sequence limit
Michael F. Stemper
10/7/13
Read Re: Sequence limit
Michael F. Stemper
10/7/13
Read Re: Sequence limit
David Bernier
10/7/13
Read Re: Sequence limit
fom
10/8/13
Read Re: Sequence limit
Virgil
10/8/13
Read Re: Sequence limit
fom
10/8/13
Read Re: Sequence limit
Virgil
10/8/13
Read Re: Sequence limit
fom
10/4/13
Read Re: Sequence limit
fom
10/4/13
Read Re: Sequence limit
quasi
10/4/13
Read Re: Sequence limit
quasi
10/9/13
Read Re: Sequence limit
Shmuel (Seymour J.) Metz
10/10/13
Read Re: Sequence limit
Bart Goddard
11/5/13
Read Re: Sequence limit
Shmuel (Seymour J.) Metz
11/6/13
Read Re: Sequence limit
Bart Goddard
11/11/13
Read Re: Sequence limit
Shmuel (Seymour J.) Metz
11/12/13
Read Re: Sequence limit
Bart Goddard
11/15/13
Read Re: Sequence limit
Shmuel (Seymour J.) Metz
11/15/13
Read Re: Sequence limit
Bart Goddard
11/6/13
Read Re: Sequence limit
Timothy Murphy
11/8/13
Read Re: Sequence limit
Bart Goddard
11/8/13
Read Re: Sequence limit
Paul
11/8/13
Read Re: Sequence limit
Bart Goddard
11/9/13
Read Re: Sequence limit
Paul
11/9/13
Read Re: Sequence limit
quasi
11/9/13
Read Re: Sequence limit
quasi
11/9/13
Read Re: Sequence limit
quasi
11/13/13
Read Re: Sequence limit
Timothy Murphy
11/13/13
Read Re: Sequence limit
quasi
11/14/13
Read Re: Sequence limit
Timothy Murphy
11/14/13
Read Re: Sequence limit
Virgil
11/14/13
Read Re: Sequence limit
Roland Franzius
11/26/13
Read Re: Sequence limit
Shmuel (Seymour J.) Metz
11/9/13
Read Re: Sequence limit
Roland Franzius
11/9/13
Read Re: Sequence limit
Paul

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