What can we conclude if limn→∞an≠0\lim_{n \to \infty} a_n \neq 0limn→∞an=0?
The series ∑n=1∞an\sum_{n=1}^{\infty} a_n∑n=1∞an converges.
The series ∑n=1∞an\sum_{n=1}^{\infty} a_n∑n=1∞an diverges by the divergence test.
The series may converge or diverge; we need more information.
The series converges absolutely.