Paper 1, Section I, E

Analysis I | Part IA, 2015

Let n0anzn\sum_{n \geqslant 0} a_{n} z^{n} be a complex power series. State carefully what it means for the power series to have radius of convergence RR, with 0R0 \leqslant R \leqslant \infty.

Find the radius of convergence of n0p(n)zn\sum_{n \geqslant 0} p(n) z^{n}, where p(n)p(n) is a fixed polynomial in nn with coefficients in C\mathbb{C}.

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