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Matrices and Determinants question

2019 · Shift 2 · Q29

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JEE Advanced
Mathematics
Matrices and Determinants
2019 · Shift 2 · Q29

Matrices and Determinants question

2019 · Shift 2 · Q29

JEE AdvancedMathematicsMatrices and DeterminantsNumerical+3 / −1

Suppose det

\left| {\begin{matrix} {\sum\limits_{k = 0}^n k } & {\sum\limits_{k = 0}^n {{}^n{C_k}{k^2}} } \\ {\sum\limits_{k = 0}^n {{}^n{C_k}.k} } & {\sum\limits_{k = 0}^n {{}^n{C_k}{3^k}} } \\ \end{matrix} } \right| = 0

holds for some positive integer n. Then

\sum\limits_{k = 0}^n {{{{}^n{C_k}} \over {k + 1}}}

equals ..............

Numerical answer

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