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, Series
*This entry contributed by Todd
Rowland*

## Explore with Wolfram|Alpha

## 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 Test## Cite this as:

Rowland, Todd. "Limit Test." From *MathWorld*--A Wolfram Web Resource, created by Eric
W. Weisstein. https://mathworld.wolfram.com/LimitTest.html