The comparison test, also called the direct comparison test, compares two series with positive terms. Let 
and 
be such series, and suppose
, 
, ....
1. If the larger series converges,
then the smaller series also converges.
2. If the smaller series diverges,
then the larger series also diverges.
See also
Convergence Tests
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References
Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 280-281,
1985.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
Comparison Test
Cite this as:
Weisstein, Eric W. "Comparison Test."
From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ComparisonTest.html
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