# Definition:Basic Null Sequence

## Definition

The sequences defined as:

• $\sequence {\dfrac 1 {n^r} }_{n \mathop \in \N}$ for $r \in \R: r > 0$
• $\sequence {\alpha^n}_{n \mathop \in \N}$ for $\alpha \in \C: \cmod {\alpha} < 1$

are known as the basic null sequences.

## Also see

That they are actually null sequences is proved in: