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In mathematics, the comparison test, sometimes called the direct comparison test is a criterion for convergence or divergence of a series whose terms are real or complex numbers. It determines convergence by comparing the terms of the series in question with those of a series whose convergence properties are known._{n} alternate in sign).
## References

## See also

The comparison test states that if the series

- $sum\_\{n=1\}^infty\; b\_n$

is an absolutely convergent series and

- $|a\_n|le\; |b\_n|$

for sufficiently large n , then the series

- $sum\_\{n=1\}^infty\; a\_n$

converges absolutely. In this case b is said to "dominate" a.

If the series

- $sum\_\{n=1\}^infty\; |b\_n|$

is divergent and

- $|a\_n|ge\; |b\_n|$

for sufficiently large n , then the series

- $sum\_\{n=1\}^infty\; a\_n$

- Knopp, Konrad, "Infinite Sequences and Series", Dover publications, Inc., New York, 1956. (§ 3.1) ISBN 0-486-60153-6
- Whittaker, E. T., and Watson, G. N., A Course in Modern Analysis, fourth edition, Cambridge University Press, 1963. (§ 2.34) ISBN 0-521-58807-3

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Last updated on Monday July 21, 2008 at 15:40:56 PDT (GMT -0700)

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