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GATE 2018 EC – Question 4

General Aptitude · Quantitative Aptitude: Arithmetic and Number Computation · 1 mark · Multiple choice

What is the value of $1+\dfrac14+\dfrac1{16}+\dfrac1{64}+\dfrac1{256}+\cdots$?

  1. 2
  2. $\frac74$
  3. $\frac32$
  4. $\frac43$

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Show answer and explanation

Correct answer: (D) $\frac43$

Explanation

This is a geometric series with first term 1 and ratio $\frac14$, so the sum is $\frac{1}{1-\frac14}=\frac43$.