# Definition:Basic Null Sequence

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## 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: