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Homework Statement
Let Ʃanx^n and Ʃbnx^n be two power series and let A and B be their converging radii. define dn=max(lanl,lcnl) and consider the series Ʃdnx^n. Show that the convergence radius of this series D, is D=min(A,B)
Homework Equations
My idea is to use that the series Ʃ(lanl+lbnl)x^n has convergence radius min(A,B) and use that lanl+lbnl≥dn. Do you agree that this is a good idea from a rigorous perspective? Last assigment I really got punished for not being rigorous enough, so I want to make sure this time, that I do it properly.