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

 Messages: [ Previous | Next ]
 Bart Goddard Posts: 1,706 Registered: 12/6/04
Re: Sequence limit
Posted: Oct 10, 2013 9:07 PM

Shmuel (Seymour J.) Metz <spamtrap@library.lspace.org.invalid> wrote in
news:52556896\$17\$fuzhry+tra\$mr2ice@news.patriot.net:

> In <XnsA24E846DE2C77goddardbenetscapenet@74.209.136.92>, on 10/03/2013
> at 06:01 PM, Bart Goddard <goddardbe@netscape.net> said:
>

>>Calculus techniques imply the answer is 1.
>

I mean that if a calculus student works the problem,
he probably elides over the difference between a
continuous and a discrete variable, sees sign,
assumes the numerator is bounded and decides the
limit of the log is zero and then concludes, almost
correctly, that the limit is 1. Since in the discrete
case, all the zeros are missed, it's likely that the
limit really is 1.

>>Anyone wrestled with the subtlies of this problem?
>
> So far you haven't shown a problem. Show your purported proof and
> maybe someone will take the time to point out the error in it.

There is no purported proof. Who knows what you're
talking about now? I purported nothing.

>>E.g., can you construct a subsequence n_k such
>>that sin (n_k) goes to zero so fast that the
>>exponent can't pull it up to 1?

>
> For all k, n_k=0. Lim k->oo |sin(n_k)|^(1/k) = 0.

Not a subsequence. But thanks for playing.

> Is this homework?

It was someone's homework. I stated the source
of the problem.

B.

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
10/4/13 quasi
10/5/13 Roland Franzius
10/5/13 quasi
10/26/13 Roland Franzius
10/26/13 karl
10/26/13 Roland Franzius
10/26/13 gnasher729
10/27/13 karl
10/3/13 quasi
10/4/13 Leon Aigret
10/4/13 William Elliot
10/4/13 quasi
10/4/13 William Elliot
10/4/13 quasi
10/4/13 David C. Ullrich
10/4/13 Robin Chapman
10/5/13 Bart Goddard
10/4/13 Bart Goddard
10/4/13 Peter Percival
10/5/13 Virgil
10/4/13 Bart Goddard
10/6/13 David Bernier
10/6/13 Virgil
10/6/13 Bart Goddard
10/7/13 Mohan Pawar
10/7/13 Bart Goddard
10/7/13 gnasher729
10/7/13 Richard Tobin
10/7/13 Robin Chapman
10/7/13 Michael F. Stemper
10/7/13 Michael F. Stemper
10/7/13 David Bernier
10/7/13 fom
10/8/13 Virgil
10/8/13 fom
10/8/13 Virgil
10/8/13 fom
10/4/13 fom
10/4/13 quasi
10/4/13 quasi
10/9/13 Shmuel (Seymour J.) Metz
10/10/13 Bart Goddard
11/5/13 Shmuel (Seymour J.) Metz
11/6/13 Bart Goddard
11/11/13 Shmuel (Seymour J.) Metz
11/12/13 Bart Goddard
11/15/13 Shmuel (Seymour J.) Metz
11/15/13 Bart Goddard
11/6/13 Timothy Murphy
11/8/13 Bart Goddard
11/8/13 Paul
11/8/13 Bart Goddard
11/9/13 Paul
11/9/13 quasi
11/9/13 quasi
11/9/13 quasi
11/13/13 Timothy Murphy
11/13/13 quasi
11/14/13 Timothy Murphy
11/14/13 Virgil
11/14/13 Roland Franzius
11/26/13 Shmuel (Seymour J.) Metz
11/9/13 Roland Franzius
11/9/13 Paul