Upper Limit
Let the greatest term 
of a Sequence be a term which is greater than all but a finite number of the termswhich 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 numberlarger than 
has this property.See also Limit, Lower Limit
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.
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