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find the radius of convergence for each of the following series. (a) (-1)n+1 (2-1-i)". Is it entire?

find the radius of convergence for each of the following series. (a) (-1)n+1 (2-1-i)". Is it entire?

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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### Problem 5: Finding the Radius of Convergence For the given problem, determine the radius of convergence for each of the following series and verify whether it is entire. #### (a) \[ \sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n!}(z - 1 - i)^n \] Is it entire? #### (b) \[ \sum_{n=1}^{\infty} \left(\frac{6n+1}{2n+5}\right)^n (z - 2i)^n \] Is it entire?
Transcribed Image Text:### Problem 5: Finding the Radius of Convergence For the given problem, determine the radius of convergence for each of the following series and verify whether it is entire. #### (a) \[ \sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n!}(z - 1 - i)^n \] Is it entire? #### (b) \[ \sum_{n=1}^{\infty} \left(\frac{6n+1}{2n+5}\right)^n (z - 2i)^n \] Is it entire?
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