Is it true $ 2^{2^n} = O(2 ^n )$?

Question

I have some problem to solve this question. Intuitively, I think not, but I'm not sure.

If a log the lelf a have $2^n \log2 <= 2^n$ That's ok ?

Answer 1

It is $\omega(2^n)$, which means that it is of higher order than $2^n$. This is easy to show if you take the limit that $\to_n \infty$.