Determine whether series is convergent or divergent $\sum_{n=1}^{\infty}\frac{1}{n^2+4}$ I still haven't gotten the hang of how to solve these problems, but when I first saw this one I thought partial fraction or limit.  So I went with taking the limit but the solution manual shows them using the integral test.  
Was I wrong to just take the limit?
$$\sum_{n=1}^{\infty}\frac{1}{n^2+4}$$
Next:
$$\lim_{n\to\infty}\frac{1}{n^2+4}=0$$
So converges by the test for divergence?

Just expounding on $\frac{1}{n^2 + 4} < \frac{1}{n^2}$ in the above answer. 
This holds using the Comparison Test which states that if $\sum a_n$ and $\sum b_n$ are such that $0 \le a_n \le b_n$, if $\sum b_n$ converges, then $\sum a_n$ converges. 
