GATE 2024 ST – Question 30

Calculus · Sequences and Series · 1 mark · Numerical answer

For Σₙ₌₀∞a_nxⁿ, coefficients satisfy a_(2n+1)=1/2^(2n+1) and a_(2n)=1/3^(2n),n≥0. Find its radius of convergence (integer).

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Correct answer: 2 to 2

Explanation

The nth-root coefficient limits along odd and even indices are 1/2 and 1/3 respectively. Cauchy–Hadamard uses the limsup 1/2, so radius R=1/(1/2)=**2**.

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