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Mathematics Question on types of differential equations

let Dk=12k2k1 nn2+n+2n2 nn2+nn2+n+2\begin{vmatrix} 1 & 2k& 2k-1\\\ n & n^2+n+2 & n^2\\\ n & n^2+n & n^2+n+2 \end{vmatrix} if k=1n∑^n_{ k=1} Dk=96, Then n is equal to

Answer

The correct Answer is: 6