# $0.9 \quad$ If $\Delta_{r}=\left|\begin{array}{ccc}r & n & 6 \\ r^{2} & 2 n^{2} & 4 n-2 \\ r^{3} & 3 n^{3} & 3 n^{2}-3 n\end{array}\right|$, then $\sum_{r=0}^{n-1} \Delta_{r}$ equals to (1) $n^{2}(n+2)$ (2) $n(n+2)^{2}$ (3) $\frac{1}{12} n\left(n^{3}+2\right)$ (4) none of these

25 views
$0.9 \quad$ If $\Delta_{r}=\left|\begin{array}{ccc}r & n & 6 \\ r^{2} & 2 n^{2} & 4 n-2 \\ r^{3} & 3 n^{3} & 3 n^{2}-3 n\end{array}\right|$, then $\sum_{r=0}^{n-1} \Delta_{r}$ equals to (1) $n^{2}(n+2)$ (2) $n(n+2)^{2}$ (3) $\frac{1}{12} n\left(n^{3}+2\right)$ (4) none of these