Allied & ICAR Exam Bank • ALLIED_0036 MCQ • 1 Mark

Section 1: Engineering Mathematics

Calculus

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

Question Statement:

The $p$-series $\sum_{n=1}^\infty \frac{1}{n^p}$ converges if and only if:

Options:

  • (A) $p > 1$
  • (B) $p \ge 1$
  • (C) $p < 1$
  • (D) $p = 1$

Answer Key:

A

Step-by-Step Solution & Explanation

By the integral test / $p$-series test, $\sum 1/n^p$ converges if $p > 1$ and diverges for $p \le 1$.
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