Question Bank • QB_EM_144 MSQ • 2 Marks

Section 1: Engineering Mathematics

Calculus

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

Question Statement:

Which of the following infinite series are CONVERGENT?

Options:

  • (A) $\sum_{n=1}^\infty \frac{1}{n^2}$
  • (B) $\sum_{n=1}^\infty \left(\frac{1}{2}\right)^n$
  • (C) $\sum_{n=1}^\infty \frac{1}{n}$
  • (D) $\sum_{n=1}^\infty \frac{1}{n^{1/2}}$

Answer Key:

A, B

Step-by-Step Solution & Explanation

- Series A is a $p$-series with $p = 2 > 1$, hence convergent. - Series B is a geometric series with common ratio $r = 1/2 < 1$, hence convergent. - Series C is the harmonic series ($p = 1$), which is divergent. - Series D is a $p$-series with $p = 0.5 \le 1$, which is divergent.
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