JEE Advanced 2019 Paper 2 Mathematics Q9

Mathematics

Problem

Suppose det [[Σₖ₌₀ⁿ k, Σₖ₌₀ⁿ ⁿCₖ k²], [Σₖ₌₀ⁿ ⁿCₖ k, Σₖ₌₀ⁿ ⁿCₖ 3ᵏ]] = 0 holds for some positive integer n. Then Σₖ₌₀ⁿ ⁿCₖ/(k + 1) equals _____.