Sequence of Powers of Number less than One/Normed Division Ring

Theorem
Let $\struct {R, \norm {\,\cdot\,}}$ be a normed division ring

Let $x \in \R$.

Let $\sequence {x_n}$ be the sequence in $\R$ defined as $x_n = x^n$.

Then:
 * $\norm{x} < 1$ $\sequence {x_n}$ is a null sequence.