If $a_n\to \infty$ and $b_n$ diverges then $a_nb_n$ diverges.
I got this statement and need to show whether it's true or false (by proving it or showing counterexample, respectively).
First of all I don't know for sure if $a_n\to\infty$ means the standard "$a_n\to +\infty$" or just "for any $c>0$ there exists $N$ such that $n\ge N \implies |a_n|>c$". I just try assuming both cases but I'm geting nowhere with any.
If $b_n\to \infty$ or $b_n\to +\infty$ or $b_n\to -\infty$ it's pretty direct in any of the cases. But I don't know how to deal with $b_n$ just assuming that it doesn't converge to any real $a$.