I hope, you can help me with the following problem:
Given the sequence (sin(n) )^n
Does is converge?
I already know, that the sequence sin(n)
(without the exponent)
is dense in [-1,1], since pi is irrational.
And I know that there is a subsequence of (sin(n))^n that converges to zero, meaning that
IF there is a limit, it has to be zero.
But so far, I have no clue, why there should be a limit. My guess is that there is no limit and that
is also dense in [-1,1], but I have no idea if thats the case and how to prove it...
I hope you can help me!