Allied & ICAR Exam Bank • ALLIED_2660 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 with first term $a = 2$ and common ratio $r = 1/4$, given by $2 + \frac{1}{2} + \frac{1}{8} + \frac{1}{32} + \dots$, evaluates to:

Answer Key:

2.67

Step-by-Step Solution & Explanation

Formula $S = \frac{a}{1 - r} = \frac{2}{1 - 0.25} = \frac{2}{0.75} = \frac{8}{3} \approx 2.667$.
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