Suppose that $(a_n)$ and $(b_n)$ are convergent sequences and that $b_n > 0$ for all $n$. Is it true that $(a_n / b_n)$ is Cauchy? If it is true, prove it. If it is not true, give a counterexample to show why it is not true.
My approach: let $lim(a_n)$ = $L$ and $\lim(b_n)$ = $M$, with $M \neq 0$. Since $(a_n)$ and $(b_n)$ converge, then by the property of limits $(a_n / b_n)$ will converge too with $M \neq 0$.
I don't know how to make it so that it is Cauchy.