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GATE 2024 DA – Question 4

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 1 mark · Multiple choice

The sum of the following infinite series is $2 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{8} + \frac{1}{9} + \frac{1}{16} + \frac{1}{27} + \cdots$

  1. 11/3
  2. 7/2
  3. 13/4
  4. 9/2

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Correct answer: (B) 7/2

Explanation

The series is made of two geometric series: the powers of $\frac{1}{2}$, namely $1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \cdots = 2$, and the powers of $\frac{1}{3}$, namely $1 + \frac{1}{3} + \frac{1}{9} + \frac{1}{27} + \cdots = \frac{3}{2}$. The sum is $2 + \frac{3}{2} = \frac{7}{2}$.