Prove that the limit lim does not exist for all n\geq 1..

Problem: 

Prove that the limit
\begin{equation} \lim_{x\to\infty}\,x^n \end{equation}
does not exist for all n\geq 1.

Answer: 

The limit \begin{equation} \lim_{x\to\infty}\,x^n \end{equation} does not exist for all n\geq 1.