Proof involving series

(a) If ∑a_n converges and lim b_n = 0, then ∑(a_n)(b_n) converges.

(b) If ∑b_n converges and lim n-> ∞ (a_n)/(b_n) = 1 then ∑ (a_n) converges.

I'm not totally sure how to do either of these. For (a), my guess is since the lim of b_n exists as a real number, 0, then (a_n)(b_n) are going to converge. Similar for (b).

are we assuming that ?

Yes.

ah well, then limit comparison test will do the job.

i'll the first one, then you should be able to do the second one.

since we'll apply limit comparison test with so so