Sequence of Powers of Number less than One/Necessary Condition

Theorem
Let $X$ be one of the standard number fields $\Q, \R, \C$.

Let $x \in X$ be such that $\left\vert{x}\right\vert < 1$.

Let $\left \langle {x_n} \right \rangle$ be the sequence in $X$ defined as $x_n = x^n$.

Then $\left \langle {x_n} \right \rangle$ is a null sequence.

Also known as
This result and Power of Reciprocal are sometimes referred to as the basic null sequences.