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 OptionsDetails 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 , a number of additional tests specific to different classes of sequences are used.
• For multiple sums, convergence tests are performed for each independent variable.

## ExamplesExamplesopen allclose all

### Basic Examples (2)Basic Examples (2)

Test for convergence of the sum :

 Out[1]=

Test the convergence of :

 Out[2]=

Find the condition for convergence of :

 Out[1]=