Let = _ k=0 ^n nk^2 k+1 and = _ k=0 ^ n-1 nk n k+1 k+2 . If 5α = 6β, then n equals ________.

JEE Main 2024 Mathematics question

Let and . If 5α = 6β, then n equals .

Answer: 10

Using ⁿCₖ/(k + 1) = ⁿ⁺¹Cₖ₊₁/(n + 1): α = (1/(n + 1))Σ ⁿ⁺¹Cₖ₊₁ ⁿCₙ₋ₖ = ²ⁿ⁺¹Cₙ₊₁/(n + 1).

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Question ID VK-017010