When the spectral radius of a matrix $B$ is less than $1$ then $B^n \to 0$ as $n$ goes to infinity Hello how to show the following fact?

When the spectral radius of a matrix $B$ is less than $1$ then $B^n \to 0$ as $n$ goes to infinity

Thank you!

There is a proof on the Wikipedia page for spectral radius.
Also there you will find the formula $\lim\limits_{n\to\infty}\|B^n\|^{1/n}$ for the spectral radius, from which this fact follows.  However, the Wikipedia article's author(s) used the result in your question to prove the formula.
