Can someone please tell me how to determine if a sequence is Cauchy without using the limit. I'm supposed to use partial fraction decomposition
$a_n=\frac{1}{n(n+1)}$. When I did the partial decomposition I found $\frac{1}{n}+\frac{1}{n+1}$ but I don't know what to do from there.
Thank you
$|a_n| <\frac 1 n$ so $|a_n-a_m|\leq |a_n|+|a_m| <\frac 1 n+\frac 1 m<\epsilon$ if $n,m >\frac 2 {\epsilon}$.