Comparison Test

Let suma_k and sumb_k be a series with positive terms and suppose a_1<=b_1, a_2<=b_2, ....

1. If the bigger series converges, then the smaller series also converges.

2. If the smaller series diverges, then the bigger series also diverges.

See also

Convergence Tests

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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.

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Comparison Test

Cite this as:

Weisstein, Eric W. "Comparison Test." From MathWorld--A Wolfram Web Resource.

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