Allied & ICAR Exam Bank • ALLIED_2659 MCQ • 1 Mark

Section 1: Engineering Mathematics

Calculus

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

Question Statement:

According to D'Alembert's ratio test, if $L = \lim_{n \to \infty} \left|\frac{a_{n+1}}{a_n}\right|$, the series $\sum a_n$ diverges when:

Options:

  • (A) $L > 1$
  • (B) $L < 1$
  • (C) $L = 1$
  • (D) $L = 0$

Answer Key:

A

Step-by-Step Solution & Explanation

The series converges absolutely for $L < 1$, diverges for $L > 1$, and the test is inconclusive for $L = 1$.
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