Prove that the limit \begin{equation} \lim_{x\to\infty}\,x^n \end{equation} 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 $n\geq 1$.