Math Help - help! show this sequence is Cauchy

1. help! show this sequence is Cauchy

Suppose that 0<r<1 and $\ \mid x_{n+1} - x_{n} \mid \$ < $r^n \ \forall n \in N$
Show that $(x_{n})$ is Cauchy.

Thank you!

2. Originally Posted by mremwo
Suppose that 0<r<1 and $\ \mid x_{n+1} - x_{n}\mid \ \forall n \in N$ Show that $(x_{n})$ is Cauchy.
There is a great deal missing here.
In fact, there is no question there what so ever.

3. yes i just edited it! sorry!

4. Some hints:

Use the generalized triangle inequality.

$\sum r^n$ is a convergent geometric series, thus the "tail" of the series can be made arbitrarily small.

5. I'm sorry, I still have no idea what to do. Could you give me another hint? This concept is very hard for me to grasp

EDIT: nevermind, i got it! thank you!