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?

It is sufficient, but not necessary, as $\lim_{n\to\infty}\frac{1}{n}=0$ but this gives the well-known harmonic series $$\sum\frac{1}{n}.$$We can check this diverges, for example, by the integral test.
