The limit test, also sometimes known as the 
th term test, says that if 
or this limit does not exist
as 
tends to infinity, then the series 
does not converge.
For example, 
does not converge by the limit test. The limit test is inconclusive when the limit
is zero.
Limit Test
See also
Convergent Series, Convergence Tests, Limit, Limit Comparison Test, Sequence, SeriesThis entry contributed by Todd Rowland
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References
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.Referenced on Wolfram|Alpha
Limit TestCite this as:
Rowland, Todd. "Limit Test." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/LimitTest.html