MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Is there any sub-sequence $n_k$ of natural numbers such as $\lim(n_k^2|\sin(n_k)|) = 0$ ? when $k$ tends to infinity. In other words, does $\lim(n^2|\sin(n)|)$ exist (equal to infinity)? or there is no such limit?

share|cite|improve this question

closed as too localized by fedja, Benjamin Steinberg, Ryan Budney, Felipe Voloch, George Lowther Dec 15 '11 at 23:17

This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet. For help making this question more broadly applicable, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.

That is equivalent to figuring out if $|\pi-\frac pq|<\frac c{q^3}$ has a solution for every $c>0$. The answer is "we don't know yet but we are getting there little by little". Currently the record for the irrationality measure of $\pi$ is 7.606..., way down from Mahler's original 30. So, just wait a couple dozen years :) – fedja Dec 15 '11 at 19:29
Most people who have thought about this believe we do know the answer but, as fedja noted, are still many years from proving it. – Noam D. Elkies Dec 15 '11 at 19:42
May I humbly suggest that fedja turns her/his comment into an answer, with perhaps some link to where the record is proven? – Julien Puydt Dec 15 '11 at 20:35
Based on fedja's comment, I'm retagging this as an open problem. I also wish John (or someone) would edit this question to "texxify" it. I don't have enough rep yet to edit. – David White Dec 15 '11 at 20:50
I mentioned this specific case in an answer to a math.SE question. – George Lowther Dec 15 '11 at 23:13