Paper 1, Section I, F

Analysis I | Part IA, 2016

Let ana_{n} be the number of pairs of integers (x,y)Z2(x, y) \in \mathbb{Z}^{2} such that x2+y2n2x^{2}+y^{2} \leqslant n^{2}. What is the radius of convergence of the series n=0anzn\sum_{n=0}^{\infty} a_{n} z^{n} ? [You may use the comparison test, provided you state it clearly.]

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