SumConvergence
SumConvergence[f,n]
gives conditions for the sum to be convergent.
SumConvergence[f,{n1,n2,…}]
gives conditions for the multiple sum to be convergent.
Details and Options

- The following options can be given:
-
Assumptions $Assumptions assumptions to make about parameters Direction 1 direction of summation Method Automatic method to use for convergence testing - Possible values for Method include:
-
"IntegralTest" the integral test "RaabeTest" Raabe's test "RatioTest" D'Alembert ratio test "RootTest" Cauchy root test - With the default setting Method->Automatic, a number of additional tests specific to different classes of sequences are used.
- For multiple sums, convergence tests are performed for each independent variable.
Examples
open allclose allBasic Examples (2)
Scope (14)
Numerical Sums (8)
Options (9)
Applications (3)
Properties & Relations (4)
Convergence properties are not affected by multiplication of constants:
Convergence is not affected by translating arguments:
SumConvergence is automatically called by Sum:
Many conditions generated by Sum are in effect convergence conditions:
With the setting VerifyConvergence->False, typically a regularized value is returned:
SumConvergence is used in sum transforms such as ZTransform:
Text
Wolfram Research (2008), SumConvergence, Wolfram Language function, https://reference.wolfram.com/language/ref/SumConvergence.html (updated 2010).
BibTeX
BibLaTeX
CMS
Wolfram Language. 2008. "SumConvergence." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2010. https://reference.wolfram.com/language/ref/SumConvergence.html.
APA
Wolfram Language. (2008). SumConvergence. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SumConvergence.html