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Consider the power series Center: a = Find the center, a, radius of convergence, R, and the interval of convergence, I. Radius: R= ∞ Σ n=1 Interval of convergence: I = (-1)^(8x - 4)" √n +1

Consider the power series Center: a = Find the center, a, radius of convergence, R, and the interval of convergence, I. Radius: R= ∞ Σ n=1 Interval of convergence: I = (-1)^(8x - 4)" √n +1

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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### Power Series Convergence Consider the power series \[ \sum_{n=1}^{\infty} \frac{(-1)^n (8x - 4)^n}{\sqrt{n + 1}}. \] Find the center, \( a \), radius of convergence, \( R \), and the interval of convergence, \( I \). **Center:** \( a = \) \[ \textinput \] **Radius:** \( R = \) \[ \textinput \] **Interval of convergence:** \( I = \) \[ \textinput \]
Transcribed Image Text:### Power Series Convergence Consider the power series \[ \sum_{n=1}^{\infty} \frac{(-1)^n (8x - 4)^n}{\sqrt{n + 1}}. \] Find the center, \( a \), radius of convergence, \( R \), and the interval of convergence, \( I \). **Center:** \( a = \) \[ \textinput \] **Radius:** \( R = \) \[ \textinput \] **Interval of convergence:** \( I = \) \[ \textinput \]
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