Consider the power series ∞ - ( z − i ) n n3n n=1 Determine its radius of convergence R. Prove that this series is not absolutely convergent on the circle |z – i| = R, and demonstrate that there exists a point zo on this circle for which the series converges.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Consider the power series
∞
-
( z − i ) n
n3n
n=1
Determine its radius of convergence R. Prove that this series is not absolutely convergent on the
circle |z – i| = R, and demonstrate that there exists a point zo on this circle for which the series
converges.
Transcribed Image Text:Consider the power series ∞ - ( z − i ) n n3n n=1 Determine its radius of convergence R. Prove that this series is not absolutely convergent on the circle |z – i| = R, and demonstrate that there exists a point zo on this circle for which the series converges.
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