The problem I have is asking me if $2^{2^{n + 1}} = O( 2^{2^n} )$?
This is my proof:
let constant $C = 16$, and $k = 1$ such that for all $n \geq k$
let $n = 1$
1: $2^{2^{1 + 1}} \leq C 2^{2^1}$
2: $2^{2^2} \leq 16 2^2$
3: $2^4 \leq 16 4$
4: $16 \leq 64$ is true. Q.E.D.
Did I properly prove that $2^{2^{n + 1}} == O( 2^{2^n} )$? Is there anything else I need to show for this proof to be complete?