## Upper Limit

Let the greatest term of a Sequence be a term which is greater than all but a finite number of the terms which are equal to . Then is called the upper limit of the Sequence.

An upper limit of a Series

is said to exist if, for every , for infinitely many values of and if no number larger than has this property.

Bromwich, T. J. I'a and MacRobert, T. M. Upper and Lower Limits of a Sequence.'' §5.1 in An Introduction to the Theory of Infinite Series, 3rd ed. New York: Chelsea, p. 40, 1991.