# Math Help - cauchy sequence

1. ## cauchy sequence

prove or disprove that if $x_n$ is Cauchy sequence with
$x_n >0 \ , \forall n \in N \ then \ \frac{1}{x_n}$
is also a Cauchy sequence .

2. Originally Posted by flower3
prove or disprove that if $x_n$ is Cauchy sequence with
$x_n >0 \ , \forall n \in N \ then \ \frac{1}{x_n}$
is also a Cauchy sequence .
What do you think? Do you have an idea as to which it may be?

3. I think the statement is false!
for example: $x_n=\frac{1}{n}$