Let $$D_k = \begin{vmatrix} 1 & 2k & 2k-1 \\ n & n^2+n+2 & n^2 \\ n & n^2+n & n^2+n+2 \end{vmatrix}$$. If $$\sum_{k=1}^{n} D_k = 96$$, then $$n$$ is equal to _____.

Correct Answer: 6

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