## Calculus 8th Edition

$\frac{1}{2}$
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 $\frac{1}{2}$.