Since for all x, that means your absolute value series will be less than the series of .
This is a convergent p-series, so by the comparison test, your series is absolutely convergent.
Could someone explain how to use what tests to determine whether the sum from n=1 to infinity of (cos(n+9)/(n^(3/2))) is absolutely convergent, conditionally convergent, or divergent? Could I use the direct comparison or limit comparison for this? If so, how; what would I compare it to?