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Let Σ1 an xn be the power series in which 2=1 An = 1 if n is a prime number 0 if n is not a prime number Prove that the series has radius of convergence 1. (Hint: you could compare with a geometric series.)

Let Σ1 an xn be the power series in which 2=1 An = 1 if n is a prime number 0 if n is not a prime number Prove that the series has radius of convergence 1. (Hint: you could compare with a geometric series.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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[Ex5 Q1] Calculus question, thanks :)

1. Let Σ‰_1 ªn x" be the power series in which -1 n An {} 1 if n is a prime number 0 if n is not a prime number Prove that the series has radius of convergence 1. Hint: you could compare with a geometric series.)
Transcribed Image Text:1. Let Σ‰_1 ªn x" be the power series in which -1 n An {} 1 if n is a prime number 0 if n is not a prime number Prove that the series has radius of convergence 1. Hint: you could compare with a geometric series.)
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