If \( D_{r}=\left|\begin{array}{ccc}2 r-1 & { }^{n} C_{r} & 1 \\ n^...

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If \( D_{r}=\left|\begin{array}{ccc}2 r-1 & { }^{n} C_{r} & 1 \\ n^{2}-1 & 2^{n} & n+1 \\ \cos ^{2}\left(n^{2}\right) & \cos ^{2} n & \cos ^{2}(n+1)\end{array}\right| \), then show that \( \sum_{r=0}^{n} D_{r}=0 \)
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