Convergence/Divergence of Series: cos(1/n)

[rcmango]

Homework Statement

question is if this series converge absolutely, converge conditionally, or it diverges?

here it is: http://img442.imageshack.us/img442/5899/untitled8tn.jpg

Homework Equations

cos1/n

The Attempt at a Solution

not sure where to start, maybe with the limit comparison test or ratio test?
please help. thanks.

 

[Gib Z]

\sum_{n=1}^{\infinity} -1^n \cos \frac{1}{n}. First check if the limit at infinity is less than 1. If each term is more than 1, it won't converge. So as we take the limit, Cos 0, its equal to 1. Since its 1, it diverges. So it can't be absolutely convergent.

For an alternating series, the last term has to converge to zero as well, so its divergent as well.

 

[rcmango]

thanks for your help.

 

[Gib Z]

No problemo :)