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$$ converges.
Prove or provide a counterexample: If $\displaystyle (s_n)$ and $\displaystyle (\frac {s_n}{t_n})$ are convergent sequences and $\displaystyle $t_n \neq 0$$ for all $\displaystyle $n$$, then $\displaystyle $t_n$$ converges.