Next, take another infinite series in which the terms may be regrouped into any order without fear of paradoxical results. For example, let a pie be divided into halves. Let one of the halves be divided in two, giving two quarters. Then let one of the two quarters be divided into two eighths. The danger of infinite series is not that they have an infinite number of terms but that they may sum to infinity.
Safety is assured if the sum of the absolute values of the terms is finite.