# Strategies for Testing Series

In general, there are no specific rules as to which test to apply to a given series.

Instead, we classify series by their form and give tips as to which tests should be considered.

This list is meant to serve as a guideline for which tests you should consider applying to a given series.

**1.** If the series is of the form

- or

- then the series is a series or a geometric series

- For the series

- it is convergent if and divergent if

- For the geometric series

- it is convergent if and divergent if

**2.** If the series has a form similar to a series or a geometric series,

- then one of the comparison tests should be considered.

**3.** If you can see that

- then you should use the Divergence Test or th term test.

**4.** If the series has the form

- or

- with for all then the Alternating Series Test should be considered.

**5.** If the series involves factorials or other products, the Ratio Test should be considered.

__NOTE:__The Ratio Test should not be used for rational functions of

- For rational functions, you should use the Limit Comparison Test.

**6.** If for some function where

- is easily evaluated, the Integral Test should be considered.

**7.** If the terms of the series are products involving powers of

- then the Root Test should be considered.

__NOTE:__ These strategies are used for determining whether a series converges or diverges.

However, these are not the strategies one should use if we are determining whether or not a

series is absolutely convergent.