Answer
$\frac{1}{2}$
Work Step by Step
A sequence is said to be converged if and only if $\lim\limits_{n \to \infty}a_{n}$ is a finite constant.
$\lim\limits_{n \to \infty}a_{n}=\lim\limits_{n \to \infty}\frac{2+n^{3}}{1+2n^{3}}$
Divide numerator and denominator by $n^{3}$.
$\lim\limits_{n \to \infty}a_{n}=\lim\limits_{n \to \infty}\frac{\frac{2+n^{3}}{n^{3}}}{\frac{1+2n^{3}}{n^{3}}}$
$=\lim\limits_{n \to \infty}\frac{\frac{2}{n^{3}}+1}{\frac{1}{n^{3}}+2}$
$=\frac{0+1}{0+2}$
$=\frac{1}{2}$
Hence, the given sequence converges to $\frac{1}{2}$.
