If Dk -1 n n 2k n2-n-1 n2-n 2k-1 n2 n2-n-1 and -k-1n Dk-56- then n equals

∴∑_k=1^n D_k=∑_k=1^n1 amp; n amp; n 2∑_k=1^nk amp; n^2+n+1 amp; n^2+n 2∑_k=1^nk ∑_k=1^n1 amp; n^2 amp; n^2+n+1 = n amp; n amp; n n ...

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Summation of Determinant

If Dk =1 n ...

Question

If $D_{k} = ∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & n & n 2 k & n^{2} + n + 1 & n^{2} + n 2 k - 1 & n^{2} & n^{2} + n + 1 \end{matrix} ∣ ∣ ∣ ∣ ∣$ and $\sum_{k = 1}^{n} D_{k} = 56$ , then n equals

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D_{k} = ∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & n & n 2 k & n^{2} + n + 1 & n^{2} + n 2 k - 1 & n^{2} & n^{2} + n + 1 \end{matrix} ∣ ∣ ∣ ∣ ∣

\sum_{k = 1}^{n} D_{k} = 56

D_{k} = |\begin{matrix} 1 & n & n \\ 2 k & n^{2} + n + 2 & n^{2} + n \\ 2 k - 1 & n^{2} & n^{2} + n + 2 \end{matrix}| and \sum_{k = 1}^{n} D_{k} = 48

D_{k} = ∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & n & n 2 k & n^{2} + n + 1 & n^{2} + n 2 k - 1 & n^{2} & n^{2} + n + 1 \end{matrix} ∣ ∣ ∣ ∣ ∣

n \sum k = 1 D_{k} = 56,

n

△_{r} = ∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & n & n 2 r & n^{2} + n + 1 & n^{2} + n 2 r - 1 & n^{2} & n^{2} + n + 1 \end{matrix} ∣ ∣ ∣ ∣ ∣

n \sum r = 1 △_{r} = 56

n

∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & n & n 2 r & n^{2} + n + 1 & n^{2} + n 2 r + 1 & n^{2} & n^{2} + n + 1 \end{matrix} ∣ ∣ ∣ ∣ ∣

\sum_{r = 1}^{n} Δ_{r} = 110

n

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