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Dirichlet’s test
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Dirichlet’s test

mathematics
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Written by
William L. Hosch
William L. Hosch was an editor at Encyclopædia Britannica.
William L. Hosch
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Key People:
Peter Gustav Lejeune Dirichlet

Dirichlet’s test, in analysis (a branch of mathematics), a test for determining if an infinite series converges to some finite value. The test was devised by the 19th-century German mathematician Peter Gustav Lejeune Dirichlet.

Let Σan be an infinite series such that its partial sums sn = a1 + a2 +⋯+ an are bounded (less than or equal to some number). And let b1, b2, b3,… be a monotonically decreasing infinite sequence (b1 ≥ b2 ≥ b3 ≥ ⋯ that converges in the limit to zero. Then the infinite series Σanbn, or a1b1 + a2b2 +⋯+ anbn+⋯ converges to some finite value. See also Abel’s test.

William L. Hosch