If \( \Delta_{r}=\left|\begin{array}{ccc}r-1 & 1 & 0 \\ 2 & r & 3+r \\ r+1 & -1 & -2\end{array}\...
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If \( \Delta_{r}=\left|\begin{array}{ccc}r-1 & 1 & 0 \\ 2 & r & 3+r \\ r+1 & -1 & -2\end{array}\right| \), find \( \sum_{r=1}^{n} \Delta_{r} \)
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