Dirichlet's test
mathematics
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Fast Facts
 Key People:
 Peter Gustav Lejeune Dirichlet
 Related Topics:
 analysis infinite series
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 19thcentury German mathematician Peter Gustav Lejeune Dirichlet.
Let Σa_{n} be an infinite series such that its partial sums s_{n} = a_{1} + a_{2} +⋯+ a_{n} are bounded (less than or equal to some number). And let b_{1}, b_{2}, b_{3},… be a monotonically decreasing infinite sequence (b_{1} ≥ b_{2} ≥ b_{3} ≥ ⋯ that converges in the limit to zero. Then the infinite series Σa_{n}b_{n}, or a_{1}b_{1} + a_{2}b_{2} +⋯+ a_{n}b_{n}+⋯ converges to some finite value. See also Abel’s test.
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