So I have this series:
$$\displaystyle\sum_{n=1}^{\infty}\frac{3n^2+15n+9}{n^4+6n^3+9n^2}$$
I noticed:
$$\displaystyle\sum_{n=1}^{\infty}\frac{1}{n^2}(\frac{3n^2+15n+9}{n^2+6n+9})$$
So can I say that it's convergent already or should I use a critera on the second fraction in the sum?
Also for sum I could use partial fractions or am I mistaken?
Any help would be appreciated.