Answer
$\lim _{n\rightarrow \infty }\dfrac {n^{2}}{n^{2}+1}=1-\dfrac {1}{n^{2}+1}=1-0=1\neq 0$
So the series diverges
Work Step by Step
$if\lim _{n\rightarrow \infty }a_{n}\neq 0\Rightarrow \sum ^{n}_{1}a_{n}$ diverges
$\lim _{n\rightarrow \infty }\dfrac {n^{2}}{n^{2}+1}=1-\dfrac {1}{n^{2}+1}=1-0=1\neq 0$
So the series diverges