Upper Limit

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

An upper limit of a series


is said to exist if, for every epsilon>0, |S_n-k|<epsilon for infinitely many values of n and if no number larger than k has this property.

See also

Limit, Lower Limit, Supremum Limit

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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.

Referenced on Wolfram|Alpha

Upper Limit

Cite this as:

Weisstein, Eric W. "Upper Limit." From MathWorld--A Wolfram Web Resource.

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