- Comment
- Use this test as a last resort. While this test is the foundation of most other tests, other tests are often easier to apply.
Alternating Series Test
- Statement
-
 and  or equivalently  converges, provided  and
- Comment
- This test applies to alternating series only.
Telescoping Series
- Statement
- Any series where massive cancellation of terms occurs. Often partial sums simplify to a sum of some early terms and some ending terms: everything in between sums to zero (cancels).
- Comment
- Any time you see individual terms involving funky arithmetic with the indices, be on the lookout for a telescoping series.
- Break up the typical term into a sum wherever possible.
- Write out the first few terms.
- Watch for developing patterns which will allow terms to cancel.
example... hide example <--/twistyPlugin twikiMakeVisibleInline-->
<--/twistyPlugin--> |