(Powers missing) Show that if ~ a"z'YI has radius of convergence R (assumed finite)

Chapter 15, Problem 15.1.31

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Show that if \(\Sigma a_{n} z^{n}\) has radius of convergence R (assumed finite), then \(\sum a_{n} z^{2 n}\) has radius of convergence \(\sqrt{R}\). Give examples.

Text Transcription:

Sigma a_{n} z^n

sum a_{n} z^{2n}

sqrt{R}