Allied & ICAR Exam Bank • ALLIED_0030 NAT • 2 Marks

Section 1: Engineering Mathematics

Calculus

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

Question Statement:

The sum of the infinite geometric series $1 + \frac{1}{3} + \frac{1}{9} + \frac{1}{27} + \dots$ is:

Answer Key:

1.5

Step-by-Step Solution & Explanation

$S_\infty = \frac{a}{1 - r} = \frac{1}{1 - 1/3} = \frac{1}{2/3} = 1.5$.
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