Q $3$

Let $a_n=\frac{3n^2-1}{n^2+4}$

a$.)$ Write the first $4$ terms of the sequence $\{a_n\}$

b$.)$ Find the first $4$ partial sums of the series ${\displaystyle \underset{n=1}{\overset{}{}}}\frac{3n^2-1}{n^2+4},\{\begin{array}{ccc}\text{:}[& ie.\text{f}\text{i}\text{n}\text{d}{s}_1,s_2,s_3,& s_4]\\ 3& \text{d}\text{e}\text{c}\text{i}\text{m}\text{a}\text{l}\text{p}\text{l}\text{a}\text{c}\text{e}\text{s}\text{.}\text{W}\text{r}\text{i}\text{t}\text{e}\text{y}\text{o}\text{u}\text{r}\text{a}\text{n}\text{s}\text{w}\text{e}\text{r}\text{s}& to\end{array}$

c$.)$ Determine if the series ${\displaystyle \underset{n=1}{\overset{}{}}}\frac{3n^2-1}{n^2+4}$ is convergent or Divergent using an appropriate test.