I'm doing a question for homework, and I am required to use the Comparison Test to test for convergence.
The series in question is:
$ \sum_{n=0}^\infty \frac {n-1}{{(n+2)}^3} $
The series I would like to compare it to is:
$ \sum_{n=1}^\infty \frac 1{{n}^2} $
My reasoning for wanting to use this series is because it is a convergent p-series that is larger than the series I am trying to test, but I am unsure if I can use it as comparison due to its divergence to $ \infty $ at n=0. I recall that with limits what is important is its behaviour as $ n\to\infty$, so does that also apply for comparing series?
Edit: Thank you to all who answered! Each one contributed to my understanding. :)