Definition:Basic Null Sequence

The sequences defined as:


 * $$\left \langle {\frac 1 {n^r}} \right \rangle_{n \in \N}$$ 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.