4) Give an example, if possible, of power series with the following properties: a) centered at Zo=3i, with radius of convergence R= 7 b) centered at Zo=1 and convergent for all z with Imz≤4, but divergent for all z with Im Z >4 ⑤centered at Zo=0 and convergent for all z with Rez = 8, but divergent for all other ZEC.
4) Give an example, if possible, of power series with the following properties: a) centered at Zo=3i, with radius of convergence R= 7 b) centered at Zo=1 and convergent for all z with Imz≤4, but divergent for all z with Im Z >4 ⑤centered at Zo=0 and convergent for all z with Rez = 8, but divergent for all other ZEC.
Chapter9: Sequences, Probability And Counting Theory
Section9.4: Series And Their Notations
Problem 10TI: Determine whether the sum of the infinite series is defined. 24+(12)+6+(3)+
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Transcribed Image Text:4) Give an example, if possible, of power series with the following
properties:
a) centered at Zo=3i, with radius of convergence R= 7
b) centered at Zo=1 and convergent for all z with Imz≤4, but
divergent for all z with Im Z >4
⑤centered at Zo=0 and convergent for all z with Rez = 8, but
divergent for all other ZEC.
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