91Ó°ÊÓ

Find the radius of convergence of the following power series: a. \(\sum_{n=0}^{\infty} z^{n !}\), b. \(\sum_{n=0}^{\infty}\left(n+2^{n}\right) z^{n}\).

Show that \(\sum_{n=1}^{\infty}\left(z^{n} / n\right)\) converges at all points on the unit circle except \(z=1 .[\) Hint \(:\) Let \(z=\) cis \(\theta\) and analyze the real and imaginary parts of the series separately.]