GATE DA 2026 Set 1 — Question 35

NAT+1 / -0EasySeriesQuantitative AptitudeGeneral Aptitude

General Aptitude → Quantitative Aptitude → Series

Last updated 5 September 2026

Question

\sum_{i=0}^{\infty} \sum_{j=1}^{\infty} 2^{-i} 3^{-j}

S = \sum_{i=0}^{\infty} \sum_{j=1}^{\infty} 2^{-i} 3^{-j} = \left( \sum_{i=0}^{\infty} \left(\frac{1}{2}\right)^i \right) \times \left( \sum_{j=1}^{\infty} \left(\frac{1}{3}\right)^j \right)

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S = \sum_{i=0}^{\infty} \sum_{j=1}^{\infty} 2^{-i} 3^{-j} = \left( \sum_{i=0}^{\infty} \left(\frac{1}{2}\right)^i \right) \times \left( \sum_{j=1}^{\infty} \left(\frac{1}{3}\right)^j \right)

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