If $\lim _{n \rightarrow \infty} a_{n}$ is not zero, then $\sum_{n=1}^{\infty} a_{n}$ does not converge.

Name: If $\lim _{n \rightarrow \infty} a_{n}$ is not zero, then $\sum_{n=1}^{\infty} a_{n}$ does not converge.
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For a series $\sum_{n=1}^{\infty} a_{n}$ to converge, a necessary condition is that $\lim _{n \rightarrow \infty} a_{n} = 0$. If this limit is not zero, the series cannot converge.

If lim⁡n→∞an\lim _{n \rightarrow \infty} a_{n}limn→∞​an​ Is Not Zero, Then ∑n=1∞an\sum_{n=1}^{\infty} a_{n}∑n=1∞​an​

If $\lim _{n \rightarrow \infty} a_{n}$ Is Not Zero, Then $\sum_{n=1}^{\infty} a_{n}$