JEE Advanced 2019 Paper 2 Mathematics Q6

Mathematics

Problem

For a ∈ ℝ, |a| > 1, let limₙ→∞ [(1 + ∛2 + ⋯ + ∛n)/(n⁷ᐟ³(1/(an + 1)² + 1/(an + 2)² + ⋯ + 1/(an + n)²))] = 54. Then the possible value(s) of a is/are