# Math Help - Infinite Series convergence or divergence

1. ## Infinite Series convergence or divergence

Please explain how to determine for the following infinite series using comparison test.

n=1, 1/n(n+2)(n+3)
We compare to 1/n^3 ??? Is it harmonic series??? p=3, is greater than 1. It means that the series converges.

Please solve this. Thank you very much

2. Originally Posted by oceanmd
Please explain how to determine for the following infinite series using comparison test.

n=1, 1/n(n+2)(n+3)
We compare to 1/n^3 ??? Is it harmonic series??? p=3, is greater than 1. It means that the series converges.

Please solve this. Thank you very much
Solve what? You just gave the answer. No, it not, strictly speaking a "harmonic series"- that is specifically 1+ 1/2+ 1/3+ 1/4+...

But you are correct that this series converges since n+2> n and n+3> n
1/(n(n+2)(n+3))< 1/n^3 and, by the "p-text" you cite, 1/n^3 converges so 1/(n(n+2)(n+3)) converges by the "comparison test".