Section 11.5

Key Problems: 3, 7, 8, 10, 12, 13, 19, 37, 42, 44

Problem 3

Test the series for convergence or divergence.

$$-\frac{2}{5}+\frac{4}{6}-\frac{6}{7}+\frac{8}{8}-\frac{10}{9}+\dots$$

Problem 7

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

Problem 8

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

Problem 10

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

Problem 12

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

Problem 13

$$\sum _{n=1}^{\infty }(-1{)}^{n-1}{e}^{2/n}$$

Problem 19

$$\sum _{n=1}^{\infty }(-1{)}^n\sin \frac{\pi }{n}$$

Problem 37

Show that the series is convergent. How many terms of the series do we need to add in order to find the sum to the indicated accuracy?

$$\sum _{n=1}^{\infty }\frac{(-1{)}^{n+1}}{n^6}(|\text{error}|<0.00005)$$

Problem 42

Approximate the sum of the series correct to four decimal places.

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

Problem 44

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