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Bertrand's Test

A convergence test also called "de Morgan's and Bertrand's test." If the ratio of terms of a series {a_n}_(n=1)^infty can be written in the form

(a_n)/(a_(n+1))=1+1/n+(rho_n)/(nlnn),

then the series converges if lim_(n->infty)__rho_n>1 and diverges if lim_(n->infty)^_rho_n<1, where lim_(n->infty)__ is the lower limit and lim_(n->infty)^_ is the upper limit.

See also

Kummer's Test

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References

Bromwich, T. J. I'A. and MacRobert, T. M. An Introduction to the Theory of Infinite Series, 3rd ed. New York: Chelsea, p. 40, 1991.

Referenced on Wolfram|Alpha

Bertrand's Test

Cite this as:

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

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