Allied & ICAR Exam Bank • ALLIED_2479 NAT • 2 Marks

Section 8: General Aptitude

Quantitative Aptitude

Subtopic: Numerical Computation

Question Statement:

The sum of the infinite series $S = 1 + \frac{2}{3} + \frac{3}{3^2} + \frac{4}{3^3} + \dots$ is:

Answer Key:

2.25

Step-by-Step Solution & Explanation

Arithmetico-geometric series: $S = \frac{a}{1-r} + \frac{dr}{(1-r)^2} = \frac{1}{1 - 1/3} + \frac{1 \times (1/3)}{(1 - 1/3)^2} = \frac{1}{2/3} + \frac{1/3}{4/9} = \frac{3}{2} + \frac{3}{4} = \frac{9}{4} = 2.25$.
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