Can it be proven that : If $a_n>0$ and $\sum a_n$ converges then $na_n \to 0$ (without assuming $a_n$ is decreasing)
Please note This question does not require $a_n$ to be decreasing as condition, Is it possible to prove $na_n \to 0$ without requiring $a_n$ to be decreasing? I keep thinking that $a_n>0$ and $\sum a_n$ converging then that implies that $a_n$ must be decreasing anyway(not monotonically decreasing necessarily )
Is it possible that $a_n>0$ and $\sum a_n$ converges then $na_n \not \to 0$?
There are already answered questions that assume $a_n$ to be decreasing as a requirement: (this question does not assume $a_n$ is decreasing)
This was the post that made me ask this question, a counter example of monotonoic decreasingness of $a_n$ was given in comments by the OP.