Expii

# Divergence Test for Series - Expii

If an infinite series converges, then the individual terms (of the underlying sequence being summed) must converge to $$0$$. This can be phrased as a simple divergence test: If $$\lim_{n\to\infty}a_n$$ either does not exist, or exists but is nonzero, then the infinite series $$\sum_n a_n$$ diverges. Otherwise, the test is inconclusive.