Confirming an answer for finding a limit I have to found the limit of the sequence $(x_n)$, which is equal to:
$((2^3-1)/(2^3+1))$ $((3^3-1)/(3^3+1))$ $...$ $((n^3-1)/(n^3+1))$,
and I used the tricks that $(n^3-1)$=$(n-1)(n^2+n+1)$, and that $(n^3+1)$=$(n+1)(n^2-n+1)$, and after cancellation, I found the limit is 2/3.  Can anyone confirm this please?  Thanks

Yes you are right!
$$\prod_{k=2}^n \dfrac{k^3 - 1}{k^3 + 1} = \dfrac{2(n^2 +n + 1)}{3n(n+1)} \to \frac{2}{3}$$
