GATE Calculus: Sequences and Series – Previous Year Questions

11 GATE previous year questions on Sequences and Series (Calculus, Statistics) with answers and explanations, from every paper.

1. GATE 2021 ST Q20 (1 mark, Numerical answer) – Find n(2n+n2n2(n/2))1/(2n-n(1/n)).
2. GATE 2022 ST Q21 (1 mark, Multiple choice) – Positive numbers a n satisfy 8/a (n+1)=7/a n+a n²/343,n≥1,a₁=3,and a n<7 for n≥2. I:a n is increasing. II:a n converges to a value in [3,7]. Which…
3. GATE 2022 ST Q37 (2 marks, Multiple choice) – Which series converge conditionally? S₁=Σ (n=0)∞(−1)n n/(n²+4); S₂=Σ (n=0)∞(−1)n(√(n²+1)−n).
4. GATE 2023 ST Q45 (2 marks, Multiple choice) – f:[0,1]→ℝ is continuous. Which statement is NOT true?
5. GATE 2023 ST Q49 (2 marks, Multiple select) – Which sets are countable?
6. GATE 2023 ST Q50 (2 marks, Multiple select) – For real a define a⁺=max(a,0),a⁻=max(−a,0). Which statements about real sequences are true?
7. GATE 2024 ST Q12 (1 mark, Multiple choice) – Let a₁=√6 and a (n+1)=√(6+a n). I:the sequence increases. II:its limit is 2. Which hold?
8. GATE 2024 ST Q30 (1 mark, Numerical answer) – For Σₙ₌₀∞a nxⁿ, coefficients satisfy a (2n+1)=1/2(2n+1) and a (2n)=1/3(2n),n≥0. Find its radius of convergence (integer).
9. GATE 2025 ST Q12 (1 mark, Multiple choice) – Which statement about countability is correct?
10. GATE 2025 ST Q47 (2 marks, Multiple select) – For n≥1, x n=1+1/√2+1/√3+⋯+1/√n−2(√n−1). Which hold?
11. GATE 2026 ST Q37 (2 marks, Multiple choice) – For x₁∈(0,4), define x (n+1)=2−√(4−x n). I:x n→0. II:x (n+1)/x n→1/4. Which hold?