Answered: In problems 2 and 3 find the radius of…

In problems 2 and 3 find the radius of convergence and interval of convergence for the given power series. 2. Problem 5.1.1.1: 2n=1

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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Question

**Educational Exercise: Finding the Radius and Interval of Convergence**

In problems 2 and 3, find the radius of convergence and interval of convergence for the given power series.

2. **Problem 5.1.1.1:**

\[\sum_{n=1}^{\infty} \frac{2^n}{n} x^n\]

3. **Problem 5.1.1.4:**

\[\sum_{k=0}^{\infty} k! (x - 1)^k\]

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