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$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.

Examples

open allclose all

Basic Examples  (2)

Test for convergence of the sum :

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Test the convergence of :

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Find the condition for convergence of :

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Scope  (14)

Options  (9)

Applications  (3)

Properties & Relations  (4)

Neat Examples  (1)

See Also

Sum  Limit  DiscreteLimit  DiscreteMaxLimit  Series  Reduce  VerifyConvergence  Regularization  DiscretePlot

Introduced in 2008
(7.0)
| Updated in 2010
(8.0)