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.

That they are actually null sequences is proved in:

• Power of Reciprocal
• Power of a Number Less Than One