Engineering Mathematics-II Unit 3 – Sequence and Series: important questions for AKTU
Unit 3 (Sequence and Series) questions that AKTU repeats most often. This unit carries about 27 marks per paper. Start with the repeated questions, then the most asked topics.
Most repeated Unit 3 questions
- Test the convergence of the following series: ∑ [1·3·5…(2n−1) / 2·4·6…(2n)] x^(2n), n=1 to ∞ (7 marks, 2025, Tests for Convergence) – also asked in 2019, 2022, 2023, 2024
- Find half range Fourier sine series of f(x) = x(π − x) in (0, π). (7 marks, 2024, Fourier Series) – also asked in 2019, 2022, 2023, 2025
- Test the convergence of the series: ∑ [1 / (n log n)²] (7 marks, 2024, Tests for Convergence) – also asked in 2019, 2022, 2023, 2025
Most important Unit 3 topic
- Fourier Series (Unit 3: Sequence and Series) – asked 10 times in 2019, 2022, 2023, 2024, 2025
Most asked Unit 3 topics
- Fourier Series – asked 10 times
- Tests for Convergence – asked 8 times
- Sequence and Series Basics – asked 4 times
More Unit 3 previous year questions
- Test the convergence of the following sequence: a_n = { 1 if n = 2^p for some p ∈ N; 1/n otherwise } (2 marks, 2025, Sequence and Series Basics)
- Examine the convergence of the following series: 1 + (α+1)/(β+1) + (α+1)(2α+1)/[(β+1)(2β+1)] + (α+1)(2α+1)(3α+1)/[(β+1)(2β+1)(3β+1)] + … (7 marks, 2025, Tests for Convergence)
- Obtain the Fourier series for the function f(x) = x², −π ≤ x ≤ π. Hence, or otherwise show that 1/1² + 1/2² + 1/3² + 1/4² + … = ∑(1/n²) = π²/6 (7 marks, 2025, Fourier Series)
- What is the constant term (a₀) in the Fourier series expansion of f(x) = x² in (−π, π)? (2 marks, 2024, Fourier Series)
- Test convergence of the series: ∑ (n!)² / (2n)! using Raabe's test. (7 marks, 2024, Tests for Convergence)
Unit 3 syllabus topics
- Sequence and Series Basics
- Tests for Convergence
- Fourier Series