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Dirichlet's Test

Let

|sum_(n=1)^pa_n|<K,
(1)

where K is independent of p. Then if f_n>=f_(n+1)>0 and

lim_(n->infty)f_n=0,
(2)

it follows that

sum_(n=1)^inftya_nf_n
(3)

converges.

See also

Convergence Tests

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Cite this as:

Weisstein, Eric W. "Dirichlet's Test." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/DirichletsTest.html

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