If U n = | array ccc n & 1 & 5 n ^ 2 & 2 ~N +1 & 2 ~N +1 n ^ 3 & 3 ~N ^ 2 & 3 ~N +1 array…
Mathematics · JEE Advanced · NTA Exams — Matrices and Determinants
If Un = \[\left|\begin{array}{ccc}
\mathrm{n} & 1 & 5 \\
\mathrm{n}^{2} & 2 \mathrm{~N}+1 & 2 \mathrm{~N}+1 \\
\mathrm{n}^{3} & 3 \mathrm{~N}^{2} & 3 \mathrm{~N}+1
\end{array}\right|\], then \(\sum_{n=1}^{N} U_{n}\)is equal to
- \(2 \sum_{n=1}^{N} n\)
- \(2 \sum_{\mathrm{n}=1}^{\mathrm{N}} \mathrm{n}^{2}\)
- \(\frac{1}{2} \sum_{n=1}^{N} n^{2}\)
- 0
Answer
(B) 2 _ n =1 ^ N n ^ 2
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