Let $\{a_{n}\}$ a sequence such that $a_{n +1}=2^{a_{n}}$, $a_{1}=1$ show that $\{a_{n}\}$ diverges to $+\infty$
hint:
It would have to prove by induction that: $a_{n}\geq 2^{n-1}$, $n = 2,3, ...$
Using the inequality $2^{n-1}=(1 +1)^{n-1}=1+(n-1)+\cdots\geq n$ (if $n\geq 2$)
Could they please explain this exercise?