JEE Advanced 2021 Paper 1 Mathematics Q15

Mathematics

Problem

For any positive integer n, let Sn: (0, ∞) → ℝ be defined by Sn(x) = Σ(k=1 to n) cot−1((1 + k(k + 1)x²)/x), where for any x ∈ ℝ, cot−1(x) ∈ (0, π) and tan−1(x) ∈ (−π/2, π/2). Then which of the following statements is (are) TRUE?

Browse the problem library