BUILT-IN MATHEMATICA SYMBOL

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 Details and Options

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.