Q: Let $\sum\limits_{n=0}^{\infty} a_n$ be a non-negative series. Which implication is true?
[A] If the series $\sum\limits_{n=0}^{\infty} a_n$ is convergent, then $\sum\limits_{n=0}^{\infty} a_n^2$ converges as well. $\leftarrow$
(B) If the series $\sum\limits_{n=0}^{\infty} a_n^5$, is convergent, then $\sum\limits_{n=0}^{\infty} a_n$ converges as well.
(C) If we allow arbitrary terms in $\sum\limits_{n=0}^{\infty} a_n$, then at least one of the implications above remains true.
Can someone please explain how they would've approached and quickly answered this question? Why is a) the solution? Is this not just the comparison test? If so, wouldn't they be claiming $a_n^2 ≤ a_n$, true iff $|a_n| \leq 1$ (but why are we able to assume this?)