Question Bank • QB_SUB_EM_0062 MSQ • 2 Marks

Section 1: Engineering Mathematics

Calculus

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

Question Statement:

Which of the following tests can establish the convergence of an infinite series of positive terms?

Options:

  • (A) D'Alembert's ratio test
  • (B) Cauchy's root test
  • (C) Integral test
  • (D) Divergence test ($n$-th term test) when $\lim a_n = 0$

Answer Key:

A, B, C

Step-by-Step Solution & Explanation

Ratio test, root test, and integral test are valid convergence criteria. The $n$-th term test can only prove divergence; $\lim a_n = 0$ is necessary but not sufficient for convergence (e.g. harmonic series).
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