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 OptionsDetails and Options

  • The following options can be given:
  • Assumptions$Assumptionsassumptions to make about parameters
    Direction1direction of summation
    MethodAutomaticmethod 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.
Introduced in 2008
(7.0)
| Updated in 2010
(8.0)