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:

• Sequence of Powers of Reciprocals is Null Sequence
• Sequence of Powers of Number less than One

• Results about basic null sequences can be found here.