Condition for divergent series When studying the material of convergent series, I came up with a question.
Is $\lim_{n \to \infty}a_n \ne 0$ a sufficient and necessary condition for the series $∑a_n$ to be divergent?

If $a_n$ does not go to $0$ as $n\to\infty$, then the sum will not converge.
However, even if it goes to $0$, the sum could still diverge, say $a_n=\cfrac{1}{n}$.
