Limit Test

The limit test, also sometimes known as the nth term test, says that if lima_n!=0 or this limit does not exist as n tends to infinity, then the series suma_n does not converge. For example, sum_(n=1)^(infty)(-1)^n does not converge by the limit test. The limit test is inconclusive when the limit is zero.

See also

Convergent Series, Convergence Tests, Limit, Limit Comparison Test, Sequence, Series

This entry contributed by Todd Rowland

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Zwillinger, D. (Ed.). "Convergence Tests." §1.3.3 in CRC Standard Mathematical Tables and Formulae, 30th ed. Boca Raton, FL: CRC Press, p. 32, 1996.

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Limit Test

Cite this as:

Rowland, Todd. "Limit Test." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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