What test should be used to determine the convergence of this series?

[rodneyram]

Homework Statement

http://i.imgur.com/1a1aT.png

Homework Equations

comparison test
alternating series test

The Attempt at a Solution

I know the limit of this is zero and it's decreasing so it's either conditionally or absolutely convergent, but I do not know what test to use so I can be sure. I tried comparing it to 1/[(n^3)+1] but its less than the series and convergent meaning the comparison test doesn't work. I tried the limit comparison test and get infinity meaning it doesn't work. What is the right way to find of this problem is absolutely or conditionally convergent?

 

[╔(σ_σ)╝]

Alternating series test.

 

[Char. Limit]

Also, it looks close to 1/n^(1.5) for sufficiently large n. That might be a good comparison.