complex sum convergence on the unit circle

Asked Jan 23 '17 at 11:23

Active Jan 23 '17 at 14:30

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I need help showing the convergence of the sum $\sum_{n=0}^\infty a_nz^n$ on the unit circle (apart from z=1) when $a_n$ is a decreasing series of real numbers such that $\lim\limits_{n\to\infty} a_n=0$ and $\sum_{n=0}^\infty a_n$ diverges.

Im kind of stuck and will very much appreciate the help.

edited Jan 23 '17 at 14:30

asked Jan 23 '17 at 11:23

roy yanai

See e.g. here (the step from $a_n = \frac{1}{n}$ to general decreasing $a_n \to 0$ is easy). – Daniel Fischer Jan 23 '17 at 14:40

complex sum convergence on the unit circle

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