Section 11.7

Key Problems: 9-15, 18, 21, 22, 23, 25, 35-37, 40

Problem 9

Test the series for convergence or divergence.

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

Problem 10

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

Problem 11

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

Problem 12

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

Problem 13

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

Problem 14

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

Problem 15

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

Problem 18

$$\sum _{n=1}^{\infty }{n}^2{e}^{-n^3}$$

Problem 21

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

Problem 22

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

Problem 23

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

Problem 25

$$\sum _{n=1}^{\infty }\frac{1\times 3\times 5\times \cdots \times (2n-1)}{2\times 5\times 8\times \cdots \times (3n-1)}$$

Problem 35

$$\sum _{n=1}^{\infty }\frac{4-\cos n}{\sqrt{n}}$$

Problem 36

$$\sum _{n=1}^{\infty }\frac{n^2+1}{5^n}$$

Problem 37

$$\sum _{k=1}^{\infty }\frac{k\ln k}{(k+1{)}^3}$$

Problem 40

$$\sum _{j=1}^{\infty }(-1{)}^j\frac{\sqrt{j}}{j+5}$$