Show that the series is absolutely convergent

[Cake]

Homework Statement

Show that
$\sum \frac {cos(\frac{n\pi} {3})} {n^2}$
is absolutely convergent, and therefore convergent

Homework Equations

Comparison test to 1/n^2

The Attempt at a Solution

So to be absulutely convergent the absolute value of the series needs to be convergent. So we compare to the series 1/n^2

$\frac {|cos(\frac{n\pi} {3})|} {n^2}/\frac{1}{n^2}$

so we take the limit as n approaches infinity of

$|cos(\frac{n\pi} {3})|$

And that's where I get stuck because the limit doesn't exist. I know this isn't a trick question because the professor is fair and let us know he wouldn't put anything to trick us on this assignment.

Where did I go wrong or go from here?

 

[haruspex]

You don't need the numerator convergent, you just need it bounded:
http://en.wikipedia.org/wiki/Convergence_tests#Direct_comparison_test
Maybe you are getting mixed up with the limit comparison test?

 

[Cake]

Got it. I thought maybe I could just stop with that but I had so much space on the page I'm thinking, "that can't be all." But yeah. That was my confusion.