Engineering Mathematics-II Unit 3 Notes AKTU (BAS203)

AKTU · BTECH · Semester 2 · Engineering Mathematics-II · Unit 3 · Notes

AKTU Engineering Mathematics-II (BAS203) Unit 3 notes for B.Tech Semester 2 – Sequence and Series. Topics: Sequence and Series Basics, Tests for…

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Unit 3: Sequence and Series – AKTU syllabus topics

Sequence and Series Basics: Convergence of Series
Tests for Convergence: Ratio and D'Alembert Test, Raabe's Test, Comparison Test
Fourier Series: Half Range Fourier Series

Q2c. Find half range sine series of f(x) = { x, 0 < x < 2; 4 − x, 2 < x < 4 } (10 marks, 2018-19)
Q5b. State D'Alembert's test. Test the series 1 + x/2 + x²/5 + x³/10 + … + xⁿ/(n² + 1) + ……… (10 marks, 2018-19)
Q2c. Test the convergence of the following series: ∑ [1·3·5…(2n−1) / 2·4·6…(2n)] x^(2n), n=1 to ∞ (7 marks, 2024-25)
Q5a. Find half range Fourier sine series of f(x) = x(π − x) in (0, π). (7 marks, 2023-24)
Q2c. Test the convergence of the series: ∑ [1 / (n log n)²] (7 marks, 2023-24)
Q1d. What is the constant term (a₀) in the Fourier series expansion of f(x) = x² in (−π, π)? (2 marks, 2023-24)
Q1e. Find the Fourier constant a₁ of f(x) = x², −π ≤ x ≤ π (2 marks, 2018-19)
Q2c. Test the series x/(1.2) + x²/(3.4) + x³/(5.6) + x⁴/(7.8) + ........ (10 marks, 2021-22)
Q5b. Obtain Fourier series for the function f(x) = { 1 + 2x/π, −π < x < 0 ; 1 − 2x/π, 0 < x < π }. Hence deduce that 1/1² + 1/3² + 1/5² + …… = π²/8. (10 marks, 2021-22)
Q5b. 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, 2024-25)

AKTU paper codes: BAS203, KAS203