If \(S_{r}=\left|\begin{array}{ccc}2 r & x & n(n+1) \\ 6 r^{2}-1 & y & n^{2}(2 n+3) \\ 4 r^{3}-2 n r & z & n^{3}(n+1)\end{array}\right|\), then the value of \(\sum_{r=1}^{n} S_{r}\) is independent of

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If \(S_{r}=\left|\begin{array}{ccc}2 r & x & n(n+1) \\ 6 r^{2}-1 & y & n^{2}(2 n+3) \\ 4 r^{3}-2 n r & z & n^{3}(n+1)\end{array}\right|\), then the value of \(\sum_{r=1}^{n} S_{r}\) is independent of

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kritika · Answer 1 · 2021-12-27T07:13:07+0000

Ans: (D)
Hint \(: \sum_{r=1}^{n} S_{r}=\left|\begin{array}{ccc}n(n+1) & x & n(n+1) \\ n^{2}(2 n+3) & y & n^{2}(2 n+3) \\ n^{3}(n+1) & z & n^{3}(n+1)\end{array}\right|=0\)

If \(S_{r}=\left|\begin{array}{ccc}2 r & x & n(n+1) \\ 6 r^{2}-1 & y & n^{2}(2 n+3) \\ 4 r^{3}-2 n r & z & n^{3}(n+1)\end{array}\right|\), then the value of \(\sum_{r=1}^{n} S_{r}\) is independent of

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