Under what condition does an infinite geometric series have a defined sum?

1. An infinite sum can only settle down if the terms being added shrink towards zero. 2. For a geometric series the terms shrink exactly when the common ratio lies strictly between -1 and 1. 3. Each successive term then affects the total less than the one before, so the running sum approaches a finite value. 4. A ratio greater than one makes the terms grow, so the sum increases without bound and is not defined. 5. The size of the first term is irrelevant, since it only scales a sum that already exists. _Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 13 "Sequences, Probability and Counting Theory", section 13.4 Series and Their Notations_