# Section 5.1 – Review of Power Series

Directions. The following are review problems for the section. It is recommended you work the problems yourself, and then click "Answer" to check your answer. If you do not understand a problem, you can click "Video" to learn how to solve it.
1. Determine the radius of convergence for the following power series:
1. $$\displaystyle \sum_{n=0}^{\infty} \frac{x^{2 n}}{n !}$$
2. $$\displaystyle \sum_{n=1}^{\infty} \frac{(-1)^{n} n^{2}(x+2)^{n}}{3^{n}}$$

1. The series converges for all $$x\in\mathbb{R}$$, so the series has an infinite radius of convergence.
2. The radius of convergence $$R=3.$$

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