$\lim \limits_ {n \to \infty} \bigg[ \large\frac{1}{1+n^3}+ \frac{4}{8+n^3}+.......+\frac{r^2}{(r^2+n^3)}+....+\frac{1}{(2n)}\bigg]$=

Question

$\begin{array}{1 1} \frac{1}{2} \log 2\\ \frac{1}{3} \log 2 \\ \log \frac{1}{2} \\ \log \frac{1}{3} \end{array} $