Definition:Basic Null Sequence

Definition
The sequences defined as:


 * $\left \langle {\dfrac 1 {n^r}} \right \rangle_{n \in \N}$ for $r \in \R: r > 0$


 * $\left \langle {\alpha^n} \right \rangle_{n \in \N}$ for $\alpha \in \C: \left|{\alpha}\right| < 1$

are known as the basic null sequences.

Also see
That they are actually null sequences is proved in:


 * Power of Reciprocal
 * Power of Number less than One