Prove or provide a counterexample: If $\displaystyle (s_n)$ and $\displaystyle (\frac {s_n}{t_n})$ are convergent sequences and $\displaystyle$t_n \neq 0$$for all \displaystyle n$$, then $\displaystyle$t_n$$converges. 2. ## Re: Convergence/Divergence Proof Originally Posted by mmstone14 Prove or provide a counterexample: If \displaystyle (s_n) and \displaystyle (\frac {s_n}{t_n}) are convergent sequences and \displaystyle t_n \neq 0$$ for all $\displaystyle$n$$, then \displaystyle t_n$$ converges.
What if $s_n=\dfrac{1}{n}~\&~t_n=n~?$