Terms go to zero

A necessary condition for a series to converge is that its terms tend to zero.

Terms go to zero

Terms go to zero: If the series $\sum_{n=1}^\infty a_n$ converges , then

\lim_{n\to\infty} a_n = 0.

Equivalently (the divergence test), if $a_n$ does not tend to $0$ , then the series $\sum_{n=1}^\infty a_n$ is divergent . This is a basic prerequisite for many convergence tests and is often used to quickly rule out convergence before applying finer criteria like the root test or ratio test .