A series $\sum a_n$ with $a_n \geq 0$ converges if and only if its partial sums are bounded above

A series $\sum a_n$ with $a_n \geq 0$ always diverges if its terms are decreasing

Non-negative series can never converge conditionally

If $a_n \geq 0$, the series converges only if $\lim a_n = 0$