EXERCISE 2.1. Suppose (an) and (bn) are sequences of complex numbers, and the series Σo anz" and Σobn" have radii of convergence R₁ and R₂, respectively. Show that the radius of convergence R of the Cauchy product of these two series satisfies R≥ min{R₁, R₂}. Give an example of two series where strict inequality holds, R > min{R₁, R₂}. (Hints: Try using Mertens' Theorem for the first part; don't overthink the last part.)

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