Answer
Converges to $5$
Work Step by Step
$a_{n}=\frac{3+5n^{2}}{n+n^{2}}$
$\lim\limits_{n \to \infty}$ $\frac{3+5n^{2}}{n+n^{2}}$ = $\lim\limits_{n \to \infty}$ $\frac{\frac{3}{n^{2}}+5}{\frac{1}{n}+1}$ = $\frac{0+5}{0+1}$ = $5$
The sequence converges to $5$.
