Let 
and 
be a series with positive
terms and suppose 
,
, ....
1. If the bigger series converges, then the smaller series also converges.
2. If the smaller series diverges, then the bigger series also diverges.
Comparison Test
See also
Convergence TestsExplore with Wolfram|Alpha
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 TestCite this as:
Weisstein, Eric W. "Comparison Test." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ComparisonTest.html