Let = _ r=0 ^ n (4r^2 + 2r + 1) nr and = ( _ r=0 ^ n nr r + 1 ) + 1 n + 1 . If 140 < 2 < 281, then the value of n is ______.

JEE Main 2024 Mathematics question

Let and . If 140 < < 281, then the value of n is .

Answer: 5

α = 4n(n + 1)2ⁿ⁻² + 2n2ⁿ⁻¹ + 2ⁿ = 2ⁿ(n² + 2n + 1) = 2ⁿ(n + 1)² and β = (2ⁿ⁺¹ − 1)/(n + 1) +

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Question ID VK-012384