How can you prove that $(a_nb_n)$ is a null sequence given that $(a_n)$ is a null sequence that converges to zero and $(b_n)$ is bounded above by $A$?
The conditions of $(a_n)$ are: For every $\varepsilon > 0$ there exists an $N$ in Natural numbers such that $|a_n| < \varepsilon$ for all $n \ge N$.
The conditions of $(b_n)$ are: $b_n$ is a function natural numbers -> reals such that there exists $A$ with $|b_n| \le A$ for all $n$ in natural numbers.