# Determining convergence of series using “Direct comparison test”

Given that $$\sum a_n\leq \sum b_n$$, if the series of $$b_n$$ converges, so does the series of $$a_n$$.

In my opinion this idea seems to be very general, because it is easy to find $$b_n$$ bigger than $$a_n$$ (both have the same domain)

Question: When finding $$b_n$$, am I bound to certain restriction?

Finding $$(b_n)$$ sometimes is more tricky than others, but you are right in that it is a fairly general idea. Nevertheless, an extremely useful one.
• $$\exists N \in \mathbb{N}$$ so that $$b_n > a_n \ \forall n > N$$
• $$\sum_{n=N}^\infty b_n < \infty$$