Section 11.8

Key Problems: 3, 6, 13, 16, 17, 23-25

Problem 3

Find the radius of convergence and interval of convergence of the power series.

$$\sum _{n=1}^{\infty }\frac{x^n}{n}$$

Problem 6

$$\sum _{n=1}^{\infty }\frac{(-1{)}^n{x}^n}{\sqrt[3]{n}}$$

Problem 13

$$\sum _{n=1}^{\infty }\frac{x^n}{n!}$$

Problem 16

$$\sum _{n=1}^{\infty }{2}^n{n}^2{x}^n$$

Problem 17

$$\sum _{n=1}^{\infty }\frac{(-1{)}^n{4}^n}{\sqrt{n}}{x}^n$$

Problem 23

$$\sum _{n=2}^{\infty }\frac{(x+2{)}^n}{2^n\ln n}$$

Problem 24

$$\sum _{n=1}^{\infty }\frac{\sqrt{n}}{8}(x+6{)}^n$$

Problem 25

$$\sum _{n=1}^{\infty }\frac{(x-2{)}^n}{n^n}$$