Allied & ICAR Exam Bank • ALLIED_2661MSQ • 2 Marks
Section 1: Engineering Mathematics
Calculus
Subtopic: Sequences and series – infinite series, tests for convergence
Question Statement:
Which of the following infinite numerical series converge to a finite real sum?
Options:
(A) $\sum_{n=1}^\infty \frac{(-1)^{n-1}}{n}$
(B) $\sum_{n=1}^\infty \frac{1}{n^2}$
(C) $\sum_{n=1}^\infty \frac{1}{n}$
(D) $\sum_{n=1}^\infty \frac{1}{2^n}$
Answer Key:
A, B, D
Step-by-Step Solution & Explanation
(A) converges by Leibniz alternating series test. (B) is a $p$-series with $p=2 > 1$. (D) is a geometric series with $r = 1/2 < 1$. (C) is the harmonic series which diverges ($p=1$).