I want to prove this example:
If $a_n \to 0$ for $n \to \infty$ and $(b_n)_n$ is bounded. Prove that $a_n \times b_n \to 0$ for $n \to \infty$.
My first guess is that I should use the definition of the boundedness and the convergence.
$|a_n| \leq M$ and $|a_n - a |< \epsilon$
My problem is, how to bring this two equations together to prove the theorem?
I appreciate your answer!!!
btw how to code in latex that the $n \to \infty$ is above the $\to$?