GATE 2026 DA – Question 35
The value of $\sum_{i=0}^{\infty}\sum_{j=1}^{\infty} 2^{-i}\,3^{-j}$ is ______________ . (*Answer in integer*)
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Correct answer: 1
Explanation
The double sum splits into a product of two geometric series. $\sum_{i=0}^{\infty} 2^{-i} = \frac{1}{1 - 1/2} = 2$ and $\sum_{j=1}^{\infty} 3^{-j} = \frac{1/3}{1 - 1/3} = \frac{1}{2}$. So the value is $2 \times \frac{1}{2} = 1$.