GATE AG 2025 • Q36 MCQ • 2 Marks

Section 1: Engineering Mathematics

Calculus

Subtopic: Sequences and series – infinite series, tests for convergence

Question Statement:

The series Σ(n=0 to r) qⁿ = 1 + q + q² + ... has the sum:

Options:

  • (A) 1/(1−q) − q^(r+1)/(1−q)
  • (B) 1/(q−1) + q^(r+1)/(q−1)
  • (C) 1/(1−q) + q^(r+1)/(1−q)
  • (D) 1/(q−1)

Official Answer Key:

A

Step-by-Step Solution & Explanation

Finite geometric sum: Σ(n=0→r) qⁿ = (1−q^(r+1))/(1−q) = 1/(1−q) − q^(r+1)/(1−q).

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