Besides using the partial sum definition of series, there are also several tests to decide whether a series converge or diverge.
- Zero test (If
, the series diverges) - Absolute convergence test (whether series is absolute convergent)
- Alternating series test (
converges if sequence is non-negative, decreasing, and converges) - Comparison test
- Root test
- Ratio test
- Integral test
- Cauchy criterion