Section Summary: 12.7

Definitions

Theorems

Properties, Hints, etc.

1. If the series is of the form

   

   then it's a p-series, converging for p>1 and diverging otherwise.

2. If the series is of the form

   

   then it's a geometric series, converging for |r|<1 and diverging otherwise.

3. If a series is similar to either of the series above, then it may be possible to use comparison with those series. Comparison may involve a judicious throwing away of stuff!

4. If

   

   then the series diverges by the Test for Divergence.

5. If the series is of the form

   

   then the Alternating Series Test is a good bet.

6. Series that involve factorials or other products may be best approached with the Ratio Test.

7. If is of the form , then the Root Test is a good candidate.

8. If , where is easily evaluated, then the Integral Test may be effective.

Summary