TOPICS
Search

Cauchy Condensation Test

Let {a_n} be a series of positive terms with a_(n+1)<=a_n. Then sum_(n=1)^(infty)a_n converges iff

sum_(k=0)^infty2^ka_(2^k)

converges.

See also

Ratio Test

This entry contributed by Jonathan Vos Post (author's link)

Explore with Wolfram|Alpha

References

Porter, G. J. "An Alternative to the Integral Test for Infinite Series." Amer. Math. Monthly 79, 634-635, 1972.Rudin, W. Principles of Mathematical Analysis, 3rd ed. New York: McGraw-Hill, pp. 61-62, 1976.

Referenced on Wolfram|Alpha

Cauchy Condensation Test

Cite this as:

Post, Jonathan Vos. "Cauchy Condensation Test." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/CauchyCondensationTest.html

Subject classifications