Is there any particular method to use when dealing with these? Let me explain my problem. For example:

Here are the rules we know:

1. The Alternating Series TestIf the series

converges if all three of the following conditions are satisfied:

a. is positive for alln.

b. for all , for some integer N.

c.

2. Absolute ConvergenceGiven if converges, we say that converges absolutely.

3. Conditional ConvergenceIf diverges, but converges, then we say that converges conditionally.

Example One:

So where do I start with an alternating series? In this instance, we know is an increasing function, so it fails part b of the alternating series test. Also approaches one as n goes to infinity. So this alternating series fails the alternating series test completely. So therefore it diverges?

Example Two

What about this one? I think this one meets of the conditions of the alternating series test. So then, if a series meets all the conditions, do I then use the conditional and absolute convergence tests? or do I just leave it at "converges by alternating series test" What is a good rule of thumb for these series?