Why I can't do:
$$\sum a_n b_n \le \sum a_n K$$
when $K$ is the bound of $b_n$ and then use the comparsion test, since $\sum a_n$ converges and therefore $\sum a_n K$ does too?
I've found Why is my proof wrong? (Rudin Ch 3 #8) If $\sum a_n$ converges, and if ${b_n}$ is monotonic and bounded, prove that $\sum a_n b_n$ converges. but mine uses the comparsion test, and this one uses epsilon delta definition