Math Help - series help

1. series help

the submation of 2n/(n+1)(n+2)(n+3)

I need to find whether it converges or diverges
Can I use the integral test for this? I am thinking of using that, would I replace the n's with x,s then find the integration and see how the limit as x goes to infinity effects the function?

2. Hello, davecs77!

$\sum^{\infty}_{n=1} \frac{2n}{(n+1)(n+2)(n+3)}$

I need to find whether it converges or diverges.
If they want simply "Converge" or "Diverge", a comparison test will suffice.

Since . $\sum \frac{2n}{(n+1)(n+2)(n+3)} \;< \;\sum \frac{2n}{n^3} \;=\;2\sum\frac{1}{n^2}$ .which is a convergent $p$-series,

. . the given series also converges.