Limit comparison test; negative outcome It says the outcome must be a positive finite answer, what happens if it's a negative finite answer? Is it inconclusive as if it were 0 or infinity?
If $\lim |a_n/b_n|=0$ and $\sum |b_n|$ converges, then $\sum |a_n|$ converges.  If $\lim |a_n/b_n|=\infty$ and $\sum |a_n|$ diverges, then $\sum |b_n|$ diverges.
I'm not sure how the above answer relates, but in my calculus 3 class our teacher, when he finds a negative result ex: -1/10 when using the limit comparison theorem, he simply combines the theorem with the absolute value theorem that says if the absolute value converges so does the series, so then you get 1/10, which is positive. Combining theorems I believe is the complicated idea here.