The value of _i=0^∈fty _j=1^∈fty 2^-i 3^-j is ______________. (Answer in integer)

GATE DA 2026 Q35: Double sum of 2^(−i) 3^(−j)

The value of $\displaystyle\sum_{i=0}^{\infty} \sum_{j=1}^{\infty} 2^{-i} 3^{-j}$ is ______________. (Answer in integer)

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Answer: 1 (official GATE 2026 final answer key)

Concept used: A double sum of a product separates into a product of geometric series.

First step: $\sum_{i \ge 0} 2^{-i} = 2$ and $\sum_{j \ge 1} 3^{-j} = \tfrac{1}{2}$ .

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Source: official GATE 2026 DA question paper and final answer key, organised by IIT Guwahati. Question paper · Answer key