CONTEXT: Uni question made up by lecturer.
If $b_n \le a_n \le 0$ and $\sum b_n$ is convergent, does this mean $\sum a_n$ is also convergent? I'm pretty sure this is true but can't work out how to apply the comparison test to it.
The comparison test states:
(1) If $\sum_{n=0}^\infty b_n$ is convergent and $0 \le a_n \le b_n$, then $\sum_{n=0}^\infty a_n$ is also convergent.
(2) If $\sum_{n=0}^\infty b_n$ is divergent and $a_n \ge b_n \ge 0$, then $\sum_{n=0}^\infty a_n$ is also divergent.
I can't apply (1) or (2) because $b_n \le a_n \le 0$ does not fit with either of these.