GATE Real Analysis: Sequences and Series of Functions – Previous Year Questions

9 GATE previous year questions on Sequences and Series of Functions (Real Analysis, Mathematics) with answers and explanations, from every paper.

1. GATE 2021 MA Q46 (2 marks, Multiple choice) – On [0,1], f n(x)=nx³e(−nx). P:(f n) is equicontinuous. Q:Σₙ₌₁∞f n does not converge uniformly. Choose truth values.
2. GATE 2022 MA Q39 (2 marks, Multiple choice) – P:if n0a nxn converges at −3 and diverges at 6, then Σ(−1)ⁿa n converges. Q:the convergence interval of n=2(-1)nxn/(4n n) is [−4,4]. Choose truth…
3. GATE 2022 MA Q40 (2 marks, Multiple choice) – On [0,1] let f n(x)=x²/[x²+(1−nx)²]. Which holds?
4. GATE 2023 MA Q13 (1 mark, Multiple choice) – Let P(x)=1+e2 ix+2e3 ix. Evaluate NN-1 k=0N-1P(k2).
5. GATE 2024 MA Q55 (2 marks, Multiple select) – Let S=f n:n≥1⊂C[0,1], f n(x)=xe(−nx), with supremum metric. Which statements hold?
6. GATE 2025 MA Q45 (2 marks, Multiple choice) – Let W be the real span of all Legendre polynomials. X=C[−1,1] with sup norm, Y=C[−1,1] with L² norm. Where is W dense?
7. GATE 2025 MA Q55 (2 marks, Multiple select) – On [0,1], f₁(x)=x/2 and f n+1=f n-12(f n2-x). Which statements hold?
8. GATE 2025 MA Q56 (2 marks, Multiple select) – For x∈(0,π), u n(x)=sin(nx)/√n. Which statements about the series hold?
9. GATE 2026 MA Q31 (1 mark, Numerical answer) – = n 01n2+( ex)n7n2+x8\,dx. Find 14α (integer).