# Sequence of Powers of Reciprocals is Null Sequence/Corollary

## Corollary to Sequence of Powers of Reciprocals is Null Sequence

Let $\sequence {x_n}$ be the sequence in $\R$ defined as:

$x_n = \dfrac 1 n$

Then $\sequence {x_n}$ is a null sequence.

## Proof

$n = n^1$ from the definition of power.

As $1 \in \Q_{>0}$ the result follows from Sequence of Powers of Reciprocals is Null Sequence.

$\blacksquare$