I have a question in the course infinitesimal calculus:

$\displaystyle a_n , b_n$ are two positive series,

$\displaystyle lim((a_n)/(b_n))=L<infinity$

Prove or give a negative example: if $\displaystyle lim(b_n)=0$, then $\displaystyle lim(a_n)=0$.

It looks very tricky, though I just couldn't find a negative example, or a way to prove it.

Can you please help me with this?