The infinite series 2 + 4 + 6 + 8 + ... has no defined sum. What word describes a series whose sum is not a real number?

1. The terms 2, 4, 6, 8 grow rather than shrink, so they never tend to zero. 2. Adding more terms therefore pushes the running total up without bound. 3. A series whose sum is not a real number is said to diverge. 4. Alternating describes a pattern of signs, not the failure of a sum to exist, so it names something else. _Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 13 "Sequences, Probability and Counting Theory", section 13.4 Series and Their Notations_