Cauchy's test for convergence

[kō·shēz ‚test fər kən′vər·jəns] (mathematics) A series is absolutely convergent if the limit as n approaches infinity of its n th term raised to the 1/ n power is less than unity. A series a_n is convergent if there exists a monotonically decreasing function ƒ such that ƒ(n) = a_n for n greater than some fixed number N, and if the integral of ƒ(x) dx from N to ∞ converges. Also known as Cauchy integral test; Maclaurin-Cauchy test.

单词	cauchy's test for convergence
释义	Cauchy's test for convergence Cauchy's test for convergence [kō·shēz ‚test fər kən′vər·jəns] (mathematics) A series is absolutely convergent if the limit as n approaches infinity of its n th term raised to the 1/ n power is less than unity. A series a_n is convergent if there exists a monotonically decreasing function ƒ such that ƒ(n) = a_n for n greater than some fixed number N, and if the integral of ƒ(x) dx from N to ∞ converges. Also known as Cauchy integral test; Maclaurin-Cauchy test.
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