Section 11.4

Key Problems: 7, 8, 10, 14, 18, 28, 30, 33, 36, 37, 41

Problem 7

Determine whether the series converges or diverges.

$$\sum _{n=1}^{\infty }\frac{1}{n^3+8}$$

Problem 8

$$\sum _{n=2}^{\infty }\frac{1}{\sqrt{n}-1}$$

Problem 10

$$\sum _{n=1}^{\infty }\frac{n-1}{n^3+1}$$

Problem 14

$$\sum _{k=1}^{\infty }\frac{k{\sin }^{2}k}{1+k^3}$$

Problem 18

$$\sum _{n=1}^{\infty }\frac{1}{\sqrt[3]{3n^4+1}}$$

Problem 28

$$\sum _{n=1}^{\infty }\frac{n+3^n}{n+2^n}$$

Problem 30

$$\sum _{n=2}^{\infty }\frac{1}{n\sqrt{n^2-1}}$$

Problem 33

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

Problem 36

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

Problem 37

$$\sum _{n=1}^{\infty }\sin \left(\frac{1}{n}\right)$$

Problem 41

Use the sum of the first 10 terms to approximate the sum of the series. Estimate the error.

$$\sum _{n=1}^{\infty }\frac{1}{5+n^5}$$