Question Bank • QB_EM_095 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) $p \le 0$

Answer Key:

A

Step-by-Step Solution & Explanation

By the integral test for p-series, $\sum_{n=1}^\infty \frac{1}{n^p}$ converges strictly when $p > 1$. For $p = 1$, it is the harmonic series which diverges to infinity.
← Previous (QB_EM_CALC_015) Next (QB_EM_ADV_037) →

Practice In Authentic CBT Exam Interface

Test your skills under authentic timed conditions with live scoring and AIR percentile ranking.

Launch CBT Mock Test