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.

**References**

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.

© 1996-9

1999-05-26