
Re: Sequence limit
Posted:
Nov 13, 2013 7:19 PM


Bart Goddard wrote:
>>> > It's clear that the upper limit is 1, >>> > since n pi mod Z will be distributed evenly in [0,1), >>> > and so will infinitely often be in the range (1/3,2/3). > >>> I don't think this is true. Sin(n) is probably >>> distributed evenly, but raising to (1/n) power is going >>> to crowd things toward 0. >> >> This sounds ambiguous to me. Do you mean that you don't think it's >> true that the upper limit is 1 or do you mean that you don't think >> it's true that it's clear that the upper limit is 1? > > Neither. Obviously the thing I don't think is true is the > sentence to which I'm responding:
> That the values > of sin n^(1/n) are evenly distributed. You could > infer this by my coment about the (1/n) power pushing > things toward zero.
You seem to be responding to yourself. I did not say that "sin n^(1/n) is evenly distributed".
> It has already been proven that the limit is 1.
I think I missed this proof. What was the essential idea?
 Timothy Murphy email: gayleard /at/ eircom.net School of Mathematics, Trinity College, Dublin 2, Ireland

