GATE 2022 MA – Question 28

Complex Analysis · Power Series and Singularities · 1 mark · Numerical answer

Find the radius of convergence of $\sum_{n\ge0}3^{n+1}z^{2n}$ to two decimals.

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Correct answer: 0.55 to 0.59

Explanation

Rewrite the series as 3Σ(3z²)ⁿ. This geometric series converges exactly for |3z²|<1, that is |z|<1/√3. Radius **0.58**.

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