Hallo everyone!

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

(sin(n))^n

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!

Greetings,

Thomas :-)